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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.
Solution
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 CPCT)
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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