37. Equal chords of a circle subtend equal angles at the centre.20

1.	37. Equal chords of a circle subtend equal angles at the centre.20
Answer» 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.

Answer»

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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