Question

Theorem 10.1 :

Equal chrods of a circle subtended equal angles at the centre..

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Answer 1

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Given:

Two equal chords AB and CD of a circle with centre O.

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To prove:

<AOB=<COD

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Proof:

The triangles AOB and COD,

OA=OC (Radii of circle)

OB=OD(Radii of a circle)

AB=CD (Given)

∴AOB≅△COD(SSS rule)

⇢<AOB=<COD(CPCT)

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Answer 2

✯Given

A circle with center O.

AB and CD are equal chords of circle

i.e. AB = CD

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✯To Prove:

∠AOB = ∠DOC

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✯Proof:

In ∆AOB & ∆DOC

AO = OD (Radius)

AB = CD (Given)

OB = OC (Radius)

ΔΑΟΒ ≈ ΔDOC (SSS rule)

ZAOB = 2 DOC (CPCT)

Hence, Proved.

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