MathDB

Parallelogram

Source: Baltic Way 2008

November 13, 2008

geometryparallelogramrhombusgeometry unsolved

Problem Statement

Let

ABCD

be a parallelogram. The circle with diameter

AC

intersects the line

BD

at points

P

and

Q

. The perpendicular to the line

AC

passing through the point

C

intersects the lines

AB

and

AD

at points

X

and

Y

, respectively. Prove that the points

P,Q,X

and

Y

lie on the same circle.

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