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2 circumcircles and a line concurrent

Source: 2013 Saudi Arabia IMO TST III p3

July 23, 2020

geometrycircumcircle

Problem Statement

Let

ABC

be an acute triangle,

M

be the midpoint of

BC

and

P

be a point on line segment

AM

. Lines

BP

and

CP

meet the circumcircle of

ABC

again at

X

and

Y

, respectively, and sides

AC

at

D

and

AB

at

E

, respectively. Prove that the circumcircles of

AXD

and

AYE

have a common point

T \ne A

on line

AM

.

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