Two Chords AB and CD of a circle with centre O, intersect each other at E. Prove that AD = CB
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From the figure there are two triangles ΔAED and ΔCEB
To prove ΔAED and ΔCEB
From the figure we get,
<AED=<CEB(Vertically opposite angles are equal)
<A=<C(since <A and <C are on the angle subtended on the same arc)
Similarly <D=<B
All angle are equal. Therefore ΔAED≅ΔCEB
To prove AD=CB
Since ΔAED≅ΔCEB
ByCPCT(Corresponding parts of congruent triangles)
AE=CE,ED=EB and AD=CB
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