Question

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

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Answer 1

Let AB and BC be 2 chords

As perpendicular drawn from centre bisects the chord

As AOBand OBC are isosceles

therefore

BOD = DOC

AOE = EOB

IN triangle EOB AND BOD

OB = OB ( COMMON)

OEB= ODB=90

EB= BD

SO EOB~BOD

SO <EOB = <BOD

2<EOB = 2<BOD

AOB= BOC

HENCE PROVED

Answer 2

ANSWER:------------

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