AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers

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AP State Syllabus 10th Class Maths Bits 9th Lesson Tangents and Secants to a Circle with Answers

Question 1.
Find the number of tangents drawn at the end points of the diameter.
Answer:
2 tangents

Question 2.
Find the area of a sector, whose radius is 7 cm and the angle is 120°.
Answer:
51.3 sq.cm
Explanation:
r = 7 cm, θ = 120°
Area of sector = \(\frac{120}{360} \times \frac{22}{7}\) x 7 x 7
= \(\frac{1}{3} \times \frac{22}{7}\) x 7 x 7
= 51.3 sq.cm.

Question 3.
If ‘r’ is the radius of a semi-circle, then find its perimeter.
Answer:
P = πr + 2r (or) r[π + 2] (or) \(\frac{36}{7}\) r

Question 4.
Write the number of parallel tangents of a circle with a given tangent.
Answer:
1 tangent

Question 5.
Write the number of secant that can be drawn to a circle.
Answer:
Infinity

AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers

Question 6.
\(\overline{\mathbf{A B}}\) is a tangent drawn to a circle with centre “O” from an external point A and B is a point of contact, then which of the following is always true ?
(i) OA > OB (ii) OA > AB (iii) AB > OB
Answer:
OA > OB and OA > AB

Question 7.
Write the angle in a semi-circle.
Answer:
90°

Question 8.
The diameter of a circle is 10.2 cm, then find its radius.
Answer:
5.1 cm
Explanation:
d = 10.2 cm, r = \(\frac{\mathrm{d}}{2}=\frac{10.2}{2}\) = 5.1 cm

Question 9.
In the given figure, ∠APB = 60° and OP = 10 cm, then find PAnswer:
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 1
Answer:
\(5 \sqrt{3}\) cm
Explanation:
In right angled triangle side QP =10 cm.
∠APO = 30°,
cos 30° = \(\frac{AP}{OP} \Rightarrow \frac{AP}{10}=\frac{\sqrt{3}}{2}\)
∴ AP = \(5 \sqrt{3}\) cm

Question 10.
PA and PB are two tangents drawn to a circle with centre ‘O’ from an exter¬nal point P. If ∠APB = 30°, then find ∠AOB.
Answer:
∠AOB = 150°

Question 11.
In the below figure,
AC = 5 cm. Find BC.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 2
Answer:
BC = 2.5 cm

Question 12.
If \(\overline{\mathbf{A P}}\) and \(\overline{\mathbf{A Q}}\) are two tangents to a circle with centre O; such that ∠POQ = 105°, then find ∠PAQ.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 3
Answer:
∠PAQ = 75°
Explanation:
∠POQ + ∠PAQ = 180°
⇒ 105° + ∠PAQ = 180°
⇒ ∠PAQ = 180°- 105° = 75°

Question 13.
Write the maximum number of possible tangents that can be drawn to a circle.
Answer:
Infinity

Question 14.
In the given figure,
∠AOB = 120°, then find ∠APO.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 4
Answer:
30°
Explanation:
∠APB = 180°- 120° = 60°
∠APO = \(\frac{\angle \mathrm{APB}}{2}=\frac{60^{\circ}}{2}\) = 30°

Question 15.
If a circle is inscribed in a Quadri-lateral, then find AB + CD.
Answer:
BC + DA

Question 16.
From the given figure,
∠APB = 40°, then find ∠AOB.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 5
Answer:
140°

Question 17.
Radius of a circle with centre ‘O’ is 5 cm. P is a point at a distance of 3 cm from ‘O’. Then with the number of tan-gents that can be drawn to the circle from the point.
Answer:
No tangents are drawn from that point (or) zero tangent.

AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers

Question 18.
Find the angle between the tangent and the radius drawn at the point of contact.
Answer:
90°

Question 19.
The centre of the circle is (2, 1) and one end of the diameter is (3, -4). Find other end of the diameter.
Answer:
(1, 6)
Explanation:
\(\frac{3+\mathrm{x}}{2}\) = 2
x =4 – 3 = 1
\(\frac{-4+y}{2}\) = 1
y = 2 + 4
y = 6
∴ Other end = (x, y) = (1, 6)

Question 20.
Find the angle made at the centre of a circle.
Answer:
360°

Question 21.
The length of a tangent to a circle from a point P is 12 cm and the radius of the circle is 5 cm, then find the distance from point P to the centre of the circle.
Answer:
13 cm
Explanation:
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 53
In right angled triangle,
OP2 = OA2 + AP2
OP2 = 52 + 122
= 25 + 144 = 169
OP = \(\sqrt{169}\) = 13 cm

Question 22.
Which of the following is not correct?
i) Maximum possible tangents that can be drawn to a circle from a point ‘p’ is 2.
ii) The number of secants drawn to a circle from a point at exterior is 2.
Answer:
Maximum possible tangents that can be drawn to a circle from a point ‘p’ is 2.

Question 23.
In the figure, AP and BP are two tangents drawn to a circle with centre ‘O’. If ∠OAB = 30°, then find ∠APB.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 6
Answer:
60°

Question 24.
In the figure PQ and PR are tangents to the circle with centre ‘O’. Then find ‘x’.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 7
Answer:
40°

Question 25.
How much the angle in a major seg¬ment ?
Answer:
An acute angle.

Question 26.
Find the area of a circle that can be inscribed in a square of side 6 cm.
Answer:
9π sq. cm

Question 27.
A tangent to a circle intersects it in …………… point (s).
Answer:
Only one point.

Question 28.
To draw a pair of tangents to a circle which are inclined to each other at an angle of 60° it is required to draw the tangents at the end points of two radii inclined at an angle of ………………
Answer:
120°

Question 29.
From the figure find ‘x’.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 8
Answer:
120° = x

Question 30.
Write the number of parallel tangents to a circle with a given tangent.
Answer:
1

Question 31.
Find the area of a square inscribed in a circle of radius 8 cm.
Answer:
128 cm2
Explanation:
Area of square inscribed in a circle having radius ‘x’ is 2x2
= 2.(8)2
= 2 x 64 = 128 cm2

AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers

Question 32.
How many tangent lines can be drawn to a circle from a point outside the circle ?
Answer:
2 tangents

Question 33.
The length of the tangents from a point ‘A’ to a circle of radius 3 cm is 4 cm, then find the distance between A and the centre of the circle.
Answer:
5 cm

Question 34.
PQ is the chord of a circle.The tangent XR drawn at X meets PQ at R when produced. IfXR =12 cm, PQ = Xcm, QR = (x – 2) cm, then find x.
Answer:
10 cm

Question 35.
Name the common point to a tangent and a circle is called.
Answer:
Point of contact.

Question 36.
If tangents PA and PB from a point ‘P’ to a circle with centre O are inclined to each other at an angle of 110°, then find ∠PAO.
Answer:
35°

Question 37.
The circumference of a circle is 100 cm. Find the side of a square inscribed in the circle.
Answer:
\(\frac{50 \sqrt{2}}{\pi}\) cm
Explanation:
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 54
Diagonal of a square = diameter By Pythagoras theorem,
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 55

Question 38.
If two tangents inclined at an angle of 60° are drawn to circle of radius 3 cm, find the length of each tangent.
Answer:
\(3 \sqrt{3}\) cm.

Question 39.
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a points Q so that OQ = 12 cm, then find PQ.
Answer:
\(\sqrt{119}\) cm

Question 40.
Write the length of the tangent drawn to a circle with radius ‘r’ from a point ‘P’ which is’d’ units from the centre.
Answer:
\(\sqrt{\mathrm{d}^{2}-r^{2}}\)

Question 41.
A circle may have …………….. parallel tangents atmost.
Answer:
2

Question 42.
In the figure PT is a tangent drawn from P. If the radius is 7 cm and OP is 25 cm, then find the length of the tangents.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 9
Answer:
24cm
Explanation:
OP2 = OT2 + PT2
⇒ 252 = 72 + PT2
⇒ PT2 = 252 – 72 = 242
⇒ PT = 24 cm

Question 43.
Write a line which intersects the given circle at two distinct points.
Answer:
Secant

Question 44.
Find the length of the tangent drawn from a point 8 cm away from the cen¬tre of a circle with radius 6 cm.
Answer:
\(2 \sqrt{7}\)cm

Question 45.
In a right triangle ABC, right angled at B, BC = 15 cm and AB = 8 cm. A circle is inscribed in the triangle ABC. Find the radius of the circle.
Answer:
3 cm
Explanation:
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 56
152 + 82 = 225 + 64 = 289
∴ AC = \(\sqrt{289}\) = 17 cm
BDIF is a square 2 (a + b + c) =15 + 17 + 8
= \(\frac{40}{2}\) = 20
∴ a = 3, b = 12, c = 5
Radius = IF = ID = IE = 3 cm.

AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers

Question 46.
If radii of two concentric circles are 6 cm and 10 cm, then find length of chord of the larger circle which is tan-gent to other is ……………..
Answer:
16 cm

Question 47.
How much the angle between the tan-gent and radius drawn through the point of contact ?
Answer:
90°

Question 48.
The semi perimeter of ΔABC = 28 cm, then find AF + BD + CE.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 10
Answer:
28 cm
Explanation:
S = 28 cm ⇒ 2S = 56 cm
Semi perimeter = AF + BD + CE
= 28 cm

Question 49.
Two circles intersect at A, B. PS, PT are two tangents drawn from P which lies on AB to the two circles, then write the relation between A, B, PS, PT.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 11
Answer:
PS = PT

Question 50.
Find the length of the tangent drawn from an exterior points is 8 cm away from the centre of a circle of radius 6 cm.
Answer:
10 cm

Question 51.
Write a line segment joining any point on a circle is called ………………..
Answer:
Chord of that circle.

Question 52.
In the figure O is the centre of the circle and PA, PB are tangents, then find their lengths.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 12
Answer:
12 cm, 12 cm

Question 53.
Find the radius of a circle is equal to the sum of the circumferences of two circles of diameters 36 cm and 20 cm.
Answer:
28 cm = r
Explanation:
r1 = 18 cm, r2 = 10 cm, r3 = ?
C1 + C2 = C3 ⇒ 2π(r1 + r2) = 2πr3
⇒ r1 + r2 = r3
⇒ 18 + 10 = r3 = 28 cm

Question 54.
In the figure, AB is a diameter and AC is chord of the circle such that ∠BAC = 30°. If DC is a tangent, then which type of ΔBCD ?
Answer:
Isosceles triangle

Question 55.
If the radii of two concentric circles are 5 cm and 13 cm, then find the length of the chord of one circle which is tangent to the other circle.
Answer:
24 cm

Question 56.
Two concentric circles of radii a and b(a>b) are given. The chord AB of larger circle touches the smaller circle at C, find the length of AB.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 13
Answer:
\(2 \sqrt{a^{2}-b^{2}}\)

Question 57.
Three circles are drawn with the ver-tices of a triangle as centres such that each circle touches the other two. If the sides of the triangle are 2 cm, 3 cm, 4 cm find the diameter of the smallest circle.
Answer:
2 cm
Explanation:
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 57
Diameter of the smallest circle is 2 cm.

Question 58.
In the figure find the value of x.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 14
Answer:
x = 5 cm

AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers

Question 59.
Find the perimeter of a quadrant of a circle of radius \(\frac { 7 }{ 2 }\) cm.
Answer:
5.5 cm
Explanation:
Perimeter of a quadrant is = \(\frac{2 \pi r}{4}\)
= \(\frac{2 \times \frac{22}{7} \times \frac{7}{2}}{4}=\frac{22}{4}=\frac{11}{2}\) = 5.5 cm.

Question 60.
Write area of circle interms of diameter.
Answer:
\(\frac{\pi \mathrm{d}^{2}}{4}\) sq.umts

Question 61.
How much the value of each angle in a square ?
Answer:
Right angle.

Question 62.
Write the sum of the central angles in a circle.
Answer:
360°

Question 63.
What do you observe from the below figure ?
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 15
Answer:
PA = PB

Question 64.
Write a formula to find area of sector.
Answer:
\(\frac{x^{0}}{360} \times \pi r^{2}\)

Question 65.
A line which is perpendicular to the radius of the circle through the point of contact is called a
Answer:
tangent

Question 66.
How much angle in a minor segment?
Answer:
Obtuse angle

Question 67.
Number of tangents drawn to a circle.
Answer:
Infinite

Question 68.
A tangent to a circle is a line which ……………. the circle exactly at one point.
Answer:
Touches

Question 69.
In how many situations a secant meets a circle ?
Answer:
At ‘2’ places

Question 70.
Find the angle between a tangent to a circle and the radius drawn at the point of contact.
Answer:
90°

Question 71.
Write a formula to find area of circle.
Answer:
πr² sq. units

Question 72.
Side of a square is 4 cm, then find
Answer:
16

Question 73.
In the figure, how much the ” value of ‘x’.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 16
Answer:
60°

Question 74.
Write a formula to find area of regu¬lar hexagon of side ‘a’ units is …………… sq. units.
Answer:
\(\frac{6 \sqrt{3}}{4} a^{2}\)

Question 75.
In the figure, AB = 6.2 cm, then find CD.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 17
Answer:
6.2 cm

AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers

Question 76.
The radius of a circle is doubled, then its area becomes …………… times.
Answer:
4

Question 77.
Angle described by hour hand in 12 hours.
Answer:
360°

Question 78.
Write a formula of area of semi-circle.
Answer:
\(\frac{\pi r^{2}}{2}\)

Question 79.
Angle made by minute hand in 1 minute.
Answer:

Explanation:
360° in 1 hour, so in 60 minutes 360°
Angle in 1 minute = \(\frac{360}{60}\) = 6°

Question 80.
In the figure, how much the value of x°.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 18
Answer:
x° = 50°
Explanation:
∠ADB = ∠ACB, so x ° = 50°

Question 81.
If AP and AQ are the two tangents to a circle with centre ‘O’. So that ∠POQ = 110°, then find ∠PAQ.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 19
Answer:
70°

Question 82.
In the figure,
BC = ………….. cm.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 20
Answer:
2.5 cm

Question 83.
The longest chord in a circle
Answer:
Diameter

Question 84.
The shaded portion in the figure represents.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 21
Answer:
Minor segment

Question 85.
Write a formula to find area of ring.
Answer:
π(R2 – r2)

Question 86.
The area of square is 49 cm2, then find its side.
Answer:
7 cm

AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers

Question 87.
How the angles in the same segment of the circle ?
Answer:
Equal

Question 88.
In the figure find the area of shaded region.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 22
Answer:
42 cm2

Question 89.
Write a formula to find perimeter of semicircle.
Answer:
\(\frac{36 r}{7}\) units

Question 90.
The given figure represents.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 23
Answer:
Isosceles trapezium

Question 91.
ABCD is a cyclic quadrilateral, then find the value of ∠A +∠C.
Answer:
180°

Question 92.
Number of chords of a circle have
Answer:
Infinite

Question 93.
In the figure, ∠ACB.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 24
Answer:
90°
Explanation:
Angle in a semi cirlce = ∠ACB = 90°

Question 94.
x° = 60°, r = 14 cm, then find area of sector.
Answer:
102.66 sq. cm

Question 95.
Find the number of tangents at one point of a circle.
Answer:
1

Question 96.
In the figure, ∠OAB.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 25
Answer:
90°

Question 97.
How much angle in a semi circle ?
Answer:
90°

Question 98.
How many tangents are drawn at the ends of a diameter of a circle ?
Answer:
Two parallel lines.

AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers

Question 99.
From the figure, then find x.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 26
Answer:
4.8 cm

Question 100.
In the figure, P is called
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 27
Answer:
Secant

Question 101.
Write the number of tangents to a circle which are parallel to secant.
Answer:
2 only

Question 102.
A tangent meets a circle in …………. points.
Answer:
1

Question 103.
How much the angle in a at the centre semi circle.
Answer:
180°

Question 104.
How the tangent drawn at the end point of radius ?
Answer:
Perpendicular to radius.

Question 105.
How many tangents can be drawn from a point inside a circle ?
Answer:
Not possible.

Question 106.
In the’figure write the relation among a, b and c.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 28
Answer:
c2 = a2 + b2

Question 107.
A bicycle wheel makes 75 revolutions per minute to maintain a speed of 8.91km per hour find diameter of the wheel.
Answer:
0.63 cm

Question 108.
In the figure, how much the value of ’a’.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 29
Answer:
a = 80°
Explanation:
∠AOB = 2∠ACB
⇒ ∠AOB = 2 x 40° = 80°

Question 109.
In the figure, x = …………… cm.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 30
Answer:
x = 8

Question 110.
In a circle, d = 10.2 cm, then find r = ……………. cm.
Answer:
5.1 cm

AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers

Question 111.
In the figure,
∠BAC = ………..?
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 31
Answer:
30°
Explanation:
∠BAC = \(\frac { 1 }{ 2 }\) ∠BOC = \(\frac { 60 }{ 2 }\) = 30°

Question 112.
Diameter of a circle passes through, …………..
Answer:
Centre

Question 113.
The shaded portion of the figure represents.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 32
Answer:
Major segment

Question 114.
Write a formula to find area of triangle.
Answer:
\(\frac { 1 }{ 2 }\) bh

Question 115.
In the figure, XY and X’Y1 are two par-allel tangents to a circle with centre ‘O’ and another tangent AB with point of contact C intersecting XY at A and X1Y1 at B, then find ∠AOB.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 33
Answer:
90°

Question 116.
In the figure, AP = 12 cm, PB = 16 cm and π = 3.14, then find perimeter of shaded region.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 34
Answer:
58

Question 117.
How many tangents are drawn from an exterior point of a circle ?
Answer:
Two tangents

Question 118.
How much the sum of opposite angles in a cyclic quadrilateral ?
Answer:
180°

Question 119.
Circles having same centre are called …………… circles.
Answer:
Concentric

Question 120.
How many circles passing through 3 collinear points in a plane ?
Answer:
No circle. .

Choose the correct answer satisfying the following statements.

Question 121.
Statement (A) : The two tangents are drawn to a circle from an external point, than they subtend equal angles at the centre.
Statement (B) : A parallelogram cir-cumscribing a circle is a rhombus.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)
Explanation:
From an external point the two tan¬gents drawn subtend equal angles at the centre. So A is true. Also, a paral¬lelogram circumscribing a circle is a rhombus, so B is also true but B is not correct explanation of Answer:
Hence, (i) is the correct option.

AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers

Question 122.
Statement (A): PA and PB are two tan-gents to a circle with centre O, such that ∠AOB =110°, then ∠APB = 90°.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 35
Statement (B) : The length of two tan-gents drawn from an external point are equal.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(iv)

Question 123.
Statement (A) : In the given figure, XA + AR = XB + BR, where XP, XQ and AB are tangents.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 36
Statement (B): A tangent to the circle can be drawn from a point inside the circle.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(ii)
Explanation:
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 58
We have XP = XQ
⇒ XA + AP = XB + BQ
⇒ XA + AR = XB + BR
[ ∵ PA =-AR and BQ = BR]
(The length of tangents drawn from in external point are equal).
So, A is correct but B is incorrect. Hence, (ii) is the correct option.

Question 124.
Statement (A) : In the given figure, a quadrilateral ABCD is drawn to cir-cumscribe a given circle, as shown. Then AB + BC = AD + DC.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 37
Statement (B) : In two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 38
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(iii)
Explanation:
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 59
We have two concentric circles (shown in fig. (b)) O is the centre of concen¬tric circles and AB is the tangent.
∴ OM ⊥ AB ⇒ AM = MB
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 60
(Perpendicular from centre ‘O’ to the chord AB bisect the chord AB)
So, A is incorrect but B is correct. Hence, (iii) is the correct option.

Question 125.
Statement (A): In the given figure, O is the centre of a circle and AT is a tan-gents at point A, then ∠BAT = 60°.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 39
Statement (B) : A straight line can meet a circle at one point only.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(ii)
Explanation:
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 61

(Angle in the semi-circle)
In AABC
∠ABC + ∠ACB + ∠CAB = 180°
⇒ 90° + 60° + ∠CAB = 180°
⇒ ∠CAB = 30°
Now, OA ⊥ AT
∵ ∠BAT = 90° – 30° = 60°
So, A is correct but B is incorrect.
Hence, (ii) is the correct option.

Question 126.
Statement (A) : If in a circle, the ra¬dius of the circle in 3 cm and distance of a point from the centre of a circle is 5 cm, then length of the tangent will be 4 cm.
Statement (B) : In a right triangle (hypotenuse)2 = (base)2 + (height)2
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)
Explanation:
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 62
(OA)2 = (AB)2 + (OB)2
AB = \(\sqrt{25-9}\) = 4 cm
Both statement (A) and statement (B) are correct. Also, statement (B) is the correct explanation of the statement (A). Option (i) is correct.

AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers

Question 127.
Statement (A) : If in a cyclic quadri¬lateral, one angle is 40°, then the opposite angle is 140°.
Statement (B): Sum of opposite angles in a cyclic quadrilateral is equal is 360°.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(ii)
Explanation:
Angle + 40° = 180°
Angle = 180°-40° = 140°
∴ A is true, B is false. Option (ii) is cor-rect.

Question 128.
Statement (A) : If length of a tangent from an external point to a circle is 8cm, then length of the other tangent from the same point is 8 cm.
Statement (B): Length of the tangents drawn from an external point to a circle are equal.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)

Question 129.
Statement (A) : If the circumference of a circle is 176 cm, then its radius is 28 cm.
Statement (B) : Circumference = 2πr radius.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true,
iv) Both A and B are false
Answer:
(i)
Explanation:
Both statement (A) and statement (B) are correct. Also statement (B) is the correct explanation of the statement (A).
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 63
Option (i) is correct.

Question 130.
Statement (A) : If the outer and inner diameter of a circular path is 10m and 6m, then area of the path is 1671 m2.
Statement (B) : If R and r be the ra¬dius of outer and inner circular path respectively, then area of path = π(R2 – r2)
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false.
Answer:
(i)
Explanation:
Both statement (A) and statement (B) are correct. Also, statement (B) is the correct explanation of the statement (A).
Area of the path = π \(\left[\left(\frac{10}{2}\right)^{2}-\left(\frac{6}{2}\right)^{2}\right]\)
= π(25 – 9) = 16π
Hence, (i) is the correct option.

Question 131.
Statement (A): If a wire of length 22 cm is bent in the shape of a circle, then area of the circle so formed is 40 cm2.
Statement (B) : Circumference of the circle = length of the wire.
i) Both A and B are true.
ii) A is true, B is false.
iii) A is false, B is true.
iv) Both A and B are false
Answer:
(iii)
Explanation:
Statement (A) is pot correct, but state-ment (B) is correct.
2πr = 22 ⇒ r = 3.5 cm
∴ Area of the circle = \(\frac{22}{7}\) x 3.5 x 3.5 = 38.5 cm2
Hence, option (iii) is correct.

Read the below passages and an¬swer to the following questions.

AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 40

In the above given figure, a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.

Question 132.
The area of the sector A’OB’is
Answer:
6π cm2
Explanation:
∠AOB = 60
Area of the sector A’OB’
= \(\frac{60}{360}\) π(6)2 = 6π cm2

Question 133.
The area of the shaded region is
Answer:
156.552 cm2
Explanation:
Area of shaded region = Area of circle + Area of ΔOAB – Area of sector A’OB’ R
= π(6)2 + \(\frac{\sqrt{3}}{4}\) (12)2 – 6π
= 36π + \(\frac{\sqrt{3}}{4}\) (144) – 6π
= 94.2 + 62.352
= 156.552 cm2

The length of two parallel chords of a circle are 6 cm and 8 cm. The smaller chord is at a distance of 4 cm from the centre.

AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers

Question 134.
The radius of the circle is
Answer:
5 cm
Explanation:
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 64
AB = 6 cm, CD = 8 cm, OM = 4 cm
AM = \(\frac { 1 }{ 2 }\) x (AB) = \(\frac { 1 }{ 2 }\) x (6) = 3 cm
In ΔOAM, By Pythagoras theorem,
OA2 = OM2 + AM2
OA = \(\sqrt{16+9}\) = 5 cm.
∴ Radius = OA = 5 cm.

Question 135.
The distance of the other chord from the centre is
Answer:
3 cm
Explanation:
CN = \(\frac { 1 }{ 2 }\) x CD = \(\frac { 1 }{ 2 }\) x 8 = 4 cm.
In ΔCON, By Pythagoras theorem,
(OC)2 = (ON)2 + (CN)2
(ON)2 = (OC)2 – (CN)2
ON = \(\sqrt{(5)^{2}-(4)^{2}}\) = 3 cm

Sohan made the following pictures also with wash basin.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 41

Question 136.
Split the shape (i) into solid combina¬tion.
Answer:
2 hemispheres + 1 square

Question 137.
Split the shape (ii) into solid figure combination.
Answer:
1 circle + 1 cylinder + 1 triangle

Question 138.
Which mathematical concept was Sohan used to find the area of objects?
Answer:
Area of circles.

Question 139.
Observe the figure, match the column.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 42
Answer:
A – (ii), B – (iii).

Question 140.
Observe the figure match the column.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 43
Answer:
A – (i), B – (iv).

Question 141.
Two circular flower beds have been shown on two sides of a square lawn ABCD of side 56m. If the centre of each circular flowered bed is the point of intersection O of the diagonals of the square lawn, then match the column.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 44
Answer:
A – (ii), B – (iii), C – (iv), D – (i).

AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers

Question 142.
Choose correct matching.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 45
Answer:
A – (i), B – (ii).

Question 143.
For a circle which is inscribed in a ΔABC having sides 8 cm, 10 cm and 12 cm. Then match the column.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 46
Answer:
A – (ii), B – (iii), C – (iv), D – (i) ,

Question 144.
If two tangents PA and PB are drawn to a circle with centre ‘O’ from an ex¬ternal point P (figure), then match the column.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 47
Answer:
A – (iii), B – (i), C – (ii), D – (iv)

Question 145.
If AB is a chord of length 6 cm, of a circle of radius 5 cm, the tangents at A and B intersects at a point X, then match the column.
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 48
Answer:
A – (iv), B – (i), C – (ii), D – (iii)

Question 146.
The length of the minutes hand of a clock is 7 cm then how much distance does it cover in one hour ?
Answer:
44 cm

Question 147.
Draw a rough diagram of minor seg¬ment of a circle and shade it.
Answer:
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 49

AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers

Question 148.
How many tangents can be drawn on a circle from a point outside the circle?
Solution:
AP 10th Class Maths Bits Chapter 9 Tangents and Secants to a Circle with Answers 50
Only two tangents can be drawn from an external point to the circle i.e., PA, PB are the two tangents to the circle.

Question 149.
What is the angle between the radius and tangent at the point of contact ?
Answer:
90°

Question 150.
What is the measure of angle at the centre in a semi circle ?
Answer:
180°