Let PQ and RS are two equal chords of a given circle and they are intersecting each other at point T
Draw perpendiculars OV and OU on these chords.
In ΔOVT and ΔOUT,
OV = OU (Equal chords of a circle are equidistant from the centre)
∠OVT = ∠OUT (Each 90°)
OT = OT (Common)
ΔOVT ≅ ΔOUT (RHS congruence rule)
∠OTV = ∠OTU (By congruent parts of congruent triangles )
Therefore, it is proved that the line joining the point of intersection to the centre makes equal angles with the chords.
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