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Question
AB and CD are two equal chords of a drde intersecting at Pas shown in fig. P is joined to O , the centre of the cirde. Prove that OP bisects ∠ CPB.
Solution
Draw perpendiculars OR and OS to CD and AB respectively.
In triangle ORP and triangle OSP
OP= OP
OR = OS (Distance of equal chords from centre are equal)
∠ PRO = ∠ PSO (right angles)
Therefore, Δ ORP ≅ Δ OSP
Hence, ∠ RPO = ∠ SPO
Thus OP bisects ∠ CPB.
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