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Question
AB and AC are two equal chords of a circle with centre o such that LABO and LCBO are equal. Prove that AB = BC.
Solution
Given: AB = AC, ∠ ABO = ∠ CBO
To Prove: AB = BC
Construction : Draw ON ⊥ AB and OM ⊥ BC
Proof : In triangles BNO and BMO,
∠ NBO = ∠ MBO (Given)
∠ BNO = ∠ BMO (Each 90 ° )
BO= BO (common)
Thus , Δ BNO ≅ Δ BMO (By AAS)
⇒ BN =BM
⇒ 2 BN = 2 BM (Since perpendicular drawn from the centre bisects the chord)
⇒ AB = BC
Hence Proved.
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