Question

Two chords AB and CD of a circle with centre O, intersect at E. If ZOEA = ZOED, prove
that AB = CD
In AABG AB = AC = 10 cm and BC = 12 cm. It is inscribed in a circle. Find the radius of​

Answer 1

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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