Question

ABCD is a cyclic quadrilateral chords AB and CD are produced to meet E show that EA.EB = EC.ED

Answer 1

Consider ΔAEC and ΔDEB on the diagram attached

<EAC = <EDB (Angles subtended on the circumference by the same chord BC)

<AEC = <DEB (Same angle for the two triangles)

<ACE = <DBE (Ii two angles of two triangles are equal, the third angles are also equal)

⇒ ΔAEC is similar to ΔDEB  and the ratios of the corresponding sides will be equal.

∴ EA/EC = ED/EB

Cross multiply:

EA.EB = EC.ED  (Proved)