MathDB

parallelogram, circle and collinear points,

Source: JBMO Shortlist 2017 G1

July 25, 2018

geometryparallelogramcollinear points

Problem Statement

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

Y

and radius

Y \ne C

intersects the line

BC

at point

X

, (

X \ne C

) and the line

DC

at point

Y

, (

Y \ne C

). Prove that the line

AX

passes through the point

Y

.

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