Given: AB and CD are the chords of a circle whose centre is O. They interest each other at P. PO is the bisector of ∠APD.
To Prove : AB = CD.
Construction: Draw OR ⊥ AB and OQ ⊥ CD.
Proof : In ∆OPR and ∆OPQ,
∠OPR = ∠OPQ [Given]
OP = OP [Common]
And ∠ORP = ∠OQP [Each = 900]
∴ ∆ORP ≅ ∆OPQ [By AAS]
∴ OR = OQ [By cpctc]
∴ AB = CD [∵Chords of a circle which are equidistant from the centre are equal]
