These AP 9th Class Maths Important Questions 12th Lesson Circles will help students prepare well for the exams.
AP State Syllabus 9th Class Maths 12th Lesson Important Questions and Answers Circles
Question 1.
In the given figure ‘O’ is the centre of the circle. \(\overline{\mathbf{A B}}\) is a chord. In ΔOAB show that ∠OAB = ∠OBA
Solution:
In ΔAOB, OA = OB = radius of circle In an isosceles triangle angles opposite to equal sides are equal angles.
∴ ∠OAB = ∠OBA
Question 2.
A chord of length of 6.2 cm is at a distance of 3.5 cm from the centre of the circle. If there is another chord of length 6.2 cm in the same circle, find the distance of the chord from it’s centre. Justify your answer.
Solution:
Given chords are equal, so they are equidistant from centre.
Distance between second chord to centre is 3.5 cm.
Question 3.
In the adjacent figure A, B, C are three points on the circle. O is it’s centre. If ∠AOB = 2x° and ∠ACB = 3x – 65°, find the value of x. Give reasons to support your answer.
Solution:
From figure ∠ACB = 3x – 65° and- ∠AOB = 2x°
From theorem, chord \(\overline{\mathrm{AB}}\) making angle at centre ∠AOB = 2∠ACB
∴ 2x = 2(3x – 65°)
2x = 6x – 130°
6x – 2x = 130°
4x = 130°
x = \(\frac{130^{\circ}}{4}\) = 32.5°
Question 4.
Read the statement. Observe the diagram then write ‘Given’ and ‘R.T.P’.
Statement : Equal chords of a circle subtend equal angles at the centre.
Solution:
Statement : Equal chords of a circle subtends equal angles at the centre.
Given : Centre of circle ‘O’, \(\overline{\mathrm{AB}}\), \(\overline{\mathrm{CD}}\) are two chords.
∠AOB, ∠COD are forming equal angles at centre.
R.T.P. : ∠AOB = ∠COD
Question 5.
Construct a circumcircle to ΔABC given with BC = 6 cm ∠A = 52° and ∠B = 48° write the steps of construction.
Solution:
Steps of construction :
→ Draw ΔXYZ with given measures.
→ Draw perpendicular bisectors to the sides of ΔXYZ, let the point of concurrence be S’.
→ Draw the circle (S, \(\overline{\mathbf{S X}}\)).
→ This is the required circumcircle.
