Theorem 10.2 Class 9 Maths Explanation with Proof

Today, we will discuss theorem 10.2 class 9 Maths which is related to Chapter 10 Circles Class 9 Mathematics. After understanding theorem 10.2, you can solve the exercise questions given in the NCERT book of Class 9 Maths.

 

 Theorem 10.2 Class 9

If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.

Given 

 A circle with centre C and radius r .∠ACB and ∠PCQ are subtended by chords AB and PQ respectively at the centre C such that ∠ACB= ∠PCQ

To Prove

Chord AB=chord PQ   

Proof 

In ∆ACB and ∆PCQ, we have

CA=CP (each= radius r)

∠ACB= ∠PCQ (given )

CB=CQ (each=radius r)

Therefore ∆ACB ≅ ∆PCQ (By SAS congruence criterion)

Hence by CPCT 

We have AB=PQ

Hence proved

Related Topics

1. Theorem 10.1

2. Theorem 10.3