# Telangana SCERT Class 9 Math Solution Chapter 12 Circles Exercise 12.2

## Telangana SCERT Solution Class IX (9) Math Chapter 12 Circles Exercise 12.2

(1) In the figure, if AB =CD and AOB = 90o find COD

Solution:

Given, AB = CD

∠AOB = 90o

AB & CD are two equal chords of the circle

∴ ∠COD = ∠AOB = 90o [∵angle subtended by two equal chords at the centre is equal]

(2.) In the figure, PQ = RS and ΟRS = 48o . Find OPQ and ROS

Solution:

Given, PQ = RS

∠ORS= 48o

In △POQ & △ROS

(i) ∠ROS = ∠POQ [∵angle subtended by equal chords of  a circle at the centre is equal]

(ii) RO = OP [radius of circle]

(iii) OS = OQ [radius of circle]

∴ △POQ ≅ △ROS by SAS

∴ ∠OPQ = ∠ORS = 48o [corresponding angles of congruent triangle are equal]

∠RSO = ∠PQO [corresponding angles of congruent △S are equal]

OR = OS [∵radius of circle]

∴In △ROS, △ORS = ∠OSR = 48o [opposite angles of equal sides are equal]

∴ ∠ORS + ∠OSR + ∠ROS = 180o [sum of angles of △ is 180o]

Or, 48 + 48 + ROS = 180o

Or, <ROS = 180o – 96o

Or, <ROS = 84o

(3) In the figure PR and QS are two diameters. Is PQ = RS?

Solution:

Given, PR and QS are two diameter of the circle

∴ O is the centre of circle since the intersection of two diameter of a circle is the centre.

∴ In △POQ & △ROS

(i) PO = OR [radius of circle]

(ii) OQ = SO [radius of circle]

(iii) ∠POQ = ∠ROS [vertically opposite angles]

∴ △POQ ≅ △ROS by SAS

∴PQ = RS [∵corresponding sides of congruent △S are equal]

Updated: October 2, 2021 — 4:34 pm