In the given figure, is the center of a circle in which chords and intersect at such that bisects Prove that
Proof
In ΔOEP and ΔOFP,
∠OEP = ∠OFP [equal to 90°]
OP = OP [common]
∠OPE = ∠OPF [OP bisects ∠BPD]
Therefore,
ΔOEP = ΔOFP [By angle-side-angle]
∴ OE = OF
AB = CD [Chords are equidistant from the center]
Hence, AB = CD Proved.