G1

Part of 2017 JBMO Shortlist

Problems(1)

parallelogram, circle and collinear points,

Source: JBMO Shortlist 2017 G1

Given a parallelogram

ABCD

. The line perpendicular to

AC

passing through

C

and the line perpendicular to

BD

passing through

A

intersect at point

P

. The circle centered at point

P

PC

intersects the line

BC

X

X \ne C

DC

Y

Y \ne C

). Prove that the line

AX

passes through the point

Y

geometryparallelogramcollinear points