equal chords of a circle subtend equal angles at the centre . proof
class 9th .
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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.
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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