MathDB

Let

ABCD

be a square (vertices labelled in clockwise order). Let

Z

be any point on diagonal

AC

between

A

and

C

such that

AZ > ZC

. Points

X

and

Y

exist such that

AXY Z

is a square (vertices labelled in clockwise order) and point

B

lies inside

AXY Z

. Let

M

be the point of intersection of lines

BX

and

DZ

(extended if necessary). Prove that

C

M

and

Y

are colinear

Problem Statement