MathDB

Let

A,B,C,D

be four points on a circle (occurring in clockwise order), with

AB<AD

and

BC>CD

. The bisectors of angles

BAD

and

BCD

meet the circle at

X

and

Y

, respectively. Consider the hexagon formed by these six points on the circle. If four of the six sides of the hexagon have equal length, prove that

BD

must be a diameter of the circle.

Problem Statement