Theorem 10.1 Class 9 Maths Explanation with Proof

Today, we will discuss theorem 10.1 class 9 Maths which is related to Chapter 10 Circles Class 9 Mathematics. After understanding theorem 10.1, you can solve the exercise questions given in the NCERT book of Class 9 Maths.

 Theorem 10.1 Class 9

Equal chords of a circle subtend equal angles at the center.

Given 

 A circle with center O

AB and CD are equal chords

To Prove 

∠AOB=∠DOC 

Proof 

In triangles AOB and DOC,

OA=OC    (Radii of a circle)

OB=OD (Radii of a circle)

AB=CD  (Given)

Therefore,      ∆AOB≅∆DOC (SSS rule )

This gives,    ∠AOB=∠DOC 

(corresponding parts of congruent triangles)

Hence proved

Related Topics

1. Theorem 10.2

2. Theorem 10.3