Q. 34.3( 285 Votes )

# 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 :

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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