Math, asked by Anu2911, 1 year ago

Prove that equal chords of a circle subtend equal angles at the centre

Answers

Answered by rohanrit
1
make two chords of equal length

prove them congruent by sss creteria

then by cpct prove that angle subtended by the two chords at center are equal
Answered by BrainlyQueen01
6
Statement : Equal chords of a circle subtend equal angles at the centre.

Given : AB and CD are chords of a circle with centre O, such that AB = CD.

To prove : ∠AOC = ∠COD

Proof :

In ΔAOB and ΔCOD,

AO = CO [radii of same circle]
BO = DO [radii of same circle]
AB = CD [given]

ΔAOB ≅ ΔCOD [SSS]
∠AOB = ∠COD [C. P. C. T]

Hence, Equal chords of a circle subtend equal angles at the centre.
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