MathDB

In a square

ABCD

, let

P

and

Q

be points on the sides

BC

and

CD

respectively, different from its endpoints, such that

BP=CQ

. Consider points

X

and

Y

such that

X\neq Y

, in the segments

AP

and

AQ

respectively. Show that, for every

X

and

Y

chosen, there exists a triangle whose sides have lengths

BX

XY

and

DY

Problem Statement