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It 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.

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Let us consider a circle with centre and  and be the chords which intersect at  

According to the question, .

We need to prove 

Drop perpendiculars  and on and respectively and join .

In triangles  and

                  (equal chords of a circle are equidistant from the centre)

                (common side)

    (both equal to )

By RHS criterion of congruence,

    (by C.P.C.T.)

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Question Text
It 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 TypeText solution:1
Upvotes150