Question

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.

Answer 1

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 ∆OVT and ∆OUT,

OV = OU (Equal chords of a circle are equidistant from the centre)

∠OVT = ∠OUT (Each 90°)

OT = OT (Common)

∠∆OVT ≅ ∠∆OUT (RHS congruence rule)

∠OTV = ∠OTU (By CPCT)

Therefore, it is proved that the line joining the point of intersection to the centre makes equal angles with the chords.