# AP 10th Class Maths 10th Chapter Circles Bits

## Chapter 10 Circles Bits for 10th Class AP Board

Multiple Choice Questions (MCQs)

Question 1.
A tangent AB at a point A to a circle of radius 5 cm meets a line through the centre O at a point B such that OB = 12 cm. Length AB is ………………. .
A) $$\sqrt{119}$$ cm
B) 12 cm
C) 7 cm
D) 12 cm
A) $$\sqrt{119}$$ cm

Question 2.
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is …………………. .
A) 49 cm
B) 7 cm
C) 9 cm
D) 24.5 cm
B) 7 cm

Question 3.
The length of the tangent from a point A at a circle of radius 3 cm, is 4 cm the distance of A from the centre of the circle is ……………….. .
A) 7 cm
B) 5 cm
C) 49 cm
D) √5 cm
B) 5 cm

Question 4.
Two equal circles touch each other externally at F and DE is a common tangent to the circles then, ∠DEF = ……………… .
A) 30°
B) 60°
C) 90°
D) 45°
C) 90°

Question 5.
PQR is a right angled triangle, right angled at Q such that QR = 6cm and PQ = 8 cm. A circle with centre O is inscribed in ΔPQR. The radius of the circle is ……………….. .
A) 14 cm
B) 10 cm
C) 3 cm
D) 2 cm
D) 2 cm

Question 6.
If four sides of a quadrilateral PQRS are tangential to a circle, then …………….. .
A) PR + PS = QS + RS
B) PQ + RS = QR + PS
C) PQ + QR = PR + QS
D) PQ + QS = PR + QR
B) PQ + RS = QR + PS

Question 7.
The length of the tangent drawn from a point 8 cm away from the centre of a circle of radius 6 cm is ………………. .
A) 10 cm
B) √7 cm
C) 3√7 cm
D) 2√7 cm
D) 2√7 cm

Question 8.
AB and CD are two common tangents to circles which touch each other at CD, if D lies on AB such that CD = 4 cm, then AB = ……………….. .
A) 6 cm
B) 4 cm
C) 9 cm
D) 8 cm
D) 8 cm

Question 9.
In the given figure, AB is a tangent to the circle with centre O. If BC = 6 cm and AB = 4 cm, then OA = ……………….

A) 5 cm
B) 12 cm
C) 3 cm
D) 7 cm
A) 5 cm

Question 10.
In the given figure perimeter of ΔADI is ……………… .

A) 77 cm
B) 30 cm
C) 40 cm
D) 27 cm
B) 30 cm

Question 11.
At one end of a diameter AB of a circle of radius 5 cm, tangent PAQ is drawn to the circle. The length of chord XY is parallel to PQ and at a distance of 8 cm from A is ……………… .
A) 4 cm
B) 5 cm
C) 8 cm
D) 6 cm
C) 8 cm

Question 12.
In the figure if PQ =12 cm, QR = 8 cm and PR = 10 cm, then AP = ……………….. .
A) 7 cm
B) 4 cm
C) 5 cm
D) 6 cm
A) 7 cm

Question 13.
In the figure AP =10 cm, then BP = ……………. .

A) $$\sqrt{136}$$ cm
B) $$\sqrt{109}$$ cm
C) $$\sqrt{127}$$ cm
D) $$\sqrt{119}$$ cm
C) $$\sqrt{127}$$ cm

Question 14.
If quadrilateral ABCD circumscribes a circle, then AN + BL = ………….. .

A) DC
B) AB
C) BC
B) AB

Question 15.
In the figure, two equal circles touch each other at P, if AB = 4.5 cm then BC = …………… .

A) 4.5 cm
B) 13.5 cm
C) 9 cm
D) 15 cm
C) 9 cm

Question 16.
In the figure, AB = 8 cm and PE = 3 cm then AE = …………….. .

A) 3 cm
B) 4 cm
C) 9 cm
D) 5 cm
D) 5 cm

Question 17.
In the figure sides of AB, BC and AC of triangle ABC, touch a circle at D, E and F respectively. If DA = 4 cm, DB = 3 cm and AC =11 cm then the length of BC = ………………. .
A) 8 cm
B) 9 cm
C) 10 cm
D) 12 cm
C) 10 cm

Question 18.
In the figure, a circle with centre O is inscribed in a quadrilateral ABCD such that it touches sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90° and DS = 5 cm then the radius of the circle is …………….. .

A) 24 cm
B) 10 cm
C) 11 cm
D) 18 cm
C) 11 cm

Question 19.
In the figure, DE and DF are tangents from an external point D to a circle with centre A. If DE = 5 cm and DE ⊥ DF then the radius of the circle is ……………… .

A) 5 cm
B) 3 cm
C) 4 cm
D) 2 cm
A) 5 cm

Question 20.
A ball is in the rest position against a step AB. If AB =10 cm and BC = 15 cm, then find diameter of the ball …………….. .

A) 5 cm
B) 25 cm
C) 22.5 cm
D) 32.5 cm
D) 32.5 cm

Question 21.
The number of pair of tangents can be drawn to a circle, which are parallel to each other, are ………………. .
A) 0
B) 2
C) 4
D) infinite
D) infinite

Question 22.
The maximum number of tangents that can be drawn to a circle from an external point is ……………… .
A) 4
B) 3
C) 2
D) 1
C) 2

Question 23.
Observe the following :
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.

Which of the following is not true ?
A) i only
B) ii only
C) i and ii
D) neither (i) nor (ii)
A) i only

Question 24.
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 the distance from point P to the centre of the circle is ……………….. .
A) 11 cm
B) 10 cm
C) 13 cm
D) 14 cm
C) 13 cm

Question 25.
From the adjacent figure ∠APB = 40°, then ∠AOB = …………….. .

A) 110°
B) 140°
C) 80°
D) 160°
B) 140°

Question 26.
If $$\overline{\mathbf{A P}}$$ and $$\overline{\mathbf{A Q}}$$ are two tangents to a circle with centre O; such that ∠POQ = 105°, then ∠PAQ =

A) 105°
B) 90°
C) 75°
D) 65°
C) 75°

Question 27.
$$\overline{\mathbf{A P}}$$ 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

A) only (i)
B) only (ii)
C) (ii) and (iii)
D) (i) and (ii)
D) (i) and (ii)

Question 28.
Number of secants that can be drawn to circle through a point inside it is
A) 0
B) 1
C) Infinite
D) 2
C) Infinite

Question 29.
Tangents PA and PB inclined at an angle 60° as shown in the figure, the ratio of lengths’of OA, OP and AP is

A) 1 : 2 : 3
B) 3 : 2 : 1
C) √3 : 2 : 1
D) 1 : 2 : √3
D) 1 : 2 : √3

Question 30.
From the given figure, ∠XOY = 130° then ∠XPO =

A) 65°
B) 35°
C) 25°
D) 55°
C) 25°

Question 31.
At point ‘P’ on a circle, PQ is a tangent and ‘O’ is the centre of the circle. If ΔOPQ is an isosceles triangle, then ∠OQP is equal to
A) 90°
B) 30°
C) 45°
D) 60°
C) 45°

Question 32.
In the given figure OA and OB are ra-dii. PA and PB are tangents to the circle at points A and B. If ∠AOB = 130°, then ∠APB = ?

A) 40°
B) 50°
C) 60°
D) 70°
B) 50°

Question 33.
If the length of a tangent from an external point ‘A’ at a distance of 5 cm from the centre of the circle is 4 cm, then the radius of the circle is ……………. .
A) 5 cm
B) 3 cm
C) 7 cm
D) 5 + √3 cm
B) 3 cm

Question 34.
In a circle, ‘O’ is the centre, P is the external point and AP is the tangent drawn to the circle from P, OA is the radius. If ∠APO = 30°, then ∠POA =?
A) 120°
B) 90°
C) 30°
D) 60°
D) 60°

Question 35.
‘O’ is the centre. PA and PB are tan-gents drawn to the circle from point P. If angle between the tangents is 60° and length of the tangent is √3 cm, then the radius of the circle is ……………. .
A) 2 cm
B) 1 cm
C) 2√3 cm
D) $$\frac{\sqrt{3}}{2}$$ cm
B) 1 cm

Question 36.
The number of secants can be drawn to a circle from an external point is ……………. .
A) Infinite
B) 1
C) 2
D) 0
A) Infinite

Fill in the blanks.

1. A tangent to a circle touches it at __________ point.
one

2. A line intersecting a circle at two points is called a __________ .
secant

3. A circle can have __________ parallel tangents at the most.
Two

4. The common point of a tangent to a circle and the circle is called __________ .
point of contact

5. There are exactly two tangents to a circle passing through a point lying __________ the circle.
outside

6. The tangents drawn at the ends of a diameter of a circle are __________ .
parallel

7. There is no tangent to a circle passing through a point lying __________ the circle.
inside

8. The length of the two tangents from an external point to a circle are __________ .
equal

9. The tangent to a circle is__________ to the radius through the point of contact.
perpendicular

10. Two circles both of radii r touch each other and each of them touches a circle of radius 2r. Then the radius of the circle which touches all the three circles is __________ .
$$\frac{2 r}{3}$$

11. Number of tangents to a circle which are parallel to a sfecant is __________ .
only two tangent parallel to a secant

12. If a regular hexagon is inscribed in a circle of radius r then its perimeter is __________ .
6r

13. AB and CD are two chords of a circle intersecting at the point P outside the circle. If PA = 12 cm, CD = 7 cm and PC = 15 cm then AB = __________ .
15.5 cm

14. AB and CD are two common tangents to circles which touch each other at point C. If D lies on AB such that CD = 4 cm then AB is __________ .
8 cm

15. In two concentric circles, if chords are drawn in the outer circle which touch the inner circle then __________ .
all chords of same length

16. Three circles of radii 1, 2 and 3 units respectively touch each other externally in the plane. The circum- radius of the triangle formed by joining the centres of the circle is __________ .
2.5 cm

17. The length of the tangent drawn from a point Q to a circle is 24 cm and the distance of Q from the centre of circle is 25 cm. The radius of circle is __________ .
7 cm

18. Number of tangents to be drawn to a circle are (is) __________ .