9th Maths 10.2

NCERT Class 9th solution of Exercise 10.1

NCERT Class 9th solution of Exercise 10.3

NCERT Class 9th solution of Exercise 10.4

NCERT Class 9th Maths Projects

Exercise 10.2

Q1. Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

Sol. :

Given:

Two equal Chords `AB` and `CD` of a circle with centre at `O`.

To Prove: 

`angleAOB=angleCOD`

Proof:

In `triangleAOB` and `triangleCOD`

`OA=OC` [Radii of a circle]

`OB=OD` [Radii of a circle]

`AB=CD` [Given]

`triangleAOBcongtriangleCOD`  [By `SSS` rule]

This gives

`angleAOB=angleCOD` [By CPCT]

Proved.

Q2. Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

Sol. :

Given:

`angleAOB=angleCOD`

To Prove:

`AB=CD`

Proof:

In `triangleAOB` and `triangleCOD`

`OA=OC`    [Radii of a circle]

`angleAOB=angleCOD` [Given]

`OB=OD`    [Radii of a circle]

`triangleAOBcongtriangleCOD` [By `SAS` rule]

This gives

`AB=CD` [By CPCT]

Proved.