AP State Syllabus AP Board 9th Class Maths Solutions Chapter 12 Circles Ex 12.2 Textbook Questions and Answers.

## AP State Syllabus 9th Class Maths Solutions 12th Lesson Circles Exercise 12.2

Question 1.

In the figure, if AB = CD and ∠AOB = 90° find ∠COD.

Solution:

‘O’ is the centre of the circle.

AB = CD (equal chords from the figure)

∴ ∠AOB = ∠COD

[ ∵ equal chords make equal angles at the centre]

∴ ∠COD = 90° [ ∵ ∠AOB = 90° given]

Question 2.

In the figure, PQ = RS and ∠ORS = 48°.

Find ∠OPQ and ∠ROS.

Solution:

‘O’ is the centre of the circle.

PQ = RS [given, equal chords]

∴∠POQ = ∠ROS [ ∵ equal chords make equal angles at the centre]

∴ In ΔROS

∠ORS + ∠OSR + ∠ROS = 180°

[angle sum property]

∴ 48° + 48° + ∠ROS = 180°

[ ∵ OR = OS(radii); ΔORS is isosceles]

∴ ∠ROS = 180° – 96° = 84°

Also ∠POQ = ∠ROS = 84°

∴ ∠OPQ = ∠OQP

[∵ OP = OQ; radii]

= \(\frac { 1 }{ 2 }\)[180°-84°] = 48°

Question 3.

In the figure, PR and QS are two diameters. Is PQ = RS ?

Solution:

‘O’ is the centre of the circle.

[ ∵ PR, QS are diameters]

OP = OR (∵ radii) .

OQ = OS (∵ radii)

∠POQ = ∠ROS [vertically opp. angles]

∴ ΔOPQ ≅ ΔORS [SAS congruence]

∴ PQ = RS [CPCT]