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Chords Equidistant from Center Are Equal

Prove the the...

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Prove the theorem of intersecting chords.

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Q. If two intersecting chords of a circle make equal angles with diameter passing through their point of intersection, prove that the chords are equal.

If two chords of a circle are equally inclined to the diameter through their point of intersection, prove that the chords are equal.

Q. If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of other chord.

A B

C D

are two chords of a circle intersecting at

P

A P \times P B = C P \times P D

.

Q. 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.

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Chords Equidistant from Center Are Equal

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