If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

Given : In circle C (O, r) equal chords AB and CD intersects at point P.
To Prove: ∠OPM = ∠OPN
Construction: Join OP. Draw OM ⊥ AB and ON ⊥CD.
Proof: In ΔOMP and ΔONP,
∠OMP = ∠ONP [∵ Each 90°]
AP = AP [∵ Common]
OM = ON [∵ Equal chords of a circle are equidistant from the centre]
Hence, ΔOMP ≅ ΔONP [∵ RHS Congruency rule]
∠OPM = ∠OPM [∵ CPCT]