MathDB

Let

ABC

be a right-angled triangle with the right angle at

B

and circumcircle

c

. Denote by

D

the midpoint of the shorter arc

AB

c

. Let

P

be the point on the side

AB

such that

CP=CD

and let

X

and

Y

be two distinct points on

c

satisfying

AX=AY=PD

. Prove that

X, Y

and

P

are collinear.
Proposed by Dominik Burek, Poland

Problem Statement