MathDB

Given five distinct points

A,M,B,C,D

in this order on the circumference of the circle

O

such that

MA=MB.

Let

P,Q

be the intersection points of the line

AC

and

MD

, and that of the line

BD

and

MC,

respectively. If two intersection points of the line

PQ

and the circumference of the circle

O

are

X,\ Y,

then prove that

MX=MY.

Problem Statement