There are two equal chords AB and and CD of a circle whose centre is O , when produced meet at point E. prove that EB=ED and EA=EC

Question

There are two equal chords AB and  and CD of a circle whose centre is O , when produced meet at point E. prove that EB=ED and EA=EC

Steve · Answer

This is clearly wrong. Suppose CD is a diameter of the circle and AB is any other chord. Then ED is the shortest distance from E to any point on the circle. ED≠EB