The given information can be represented diagrammatically as:

In this figure AB and CD are two chords intersect at point P. O is the centre of the circle. XY is the diameter of the circle passes through point P.

Given that ∠OPM = ∠OPN

Let OM⊥AB and ON⊥CD

In ∆OMP and ∆ONP

∠OMP = ∠ONP (Each 90°)

∠OPM = ∠OPN (Given)

OP = OP (Common)

∴ ∆OMP ≅ ∆ONP (AAS congruence criterion)

⇒ OM = ON (C.P.C.T)

Since the chords AB and CD are equidistant from the centre of the circle so, the chords AB and CD are equal

∴AB = CD