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concyclic wanted, starting with a #, a circle and a perpendicular

Source: 2008 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p11

April 28, 2021

geometryparallelogramConcyclicUkraine Correspondence

Problem Statement

Let

ABCD

be a parallelogram. A circle with diameter

AC

intersects line

BD

at points

P

and

Q

. The perpendicular on

AC

passing through point

C

, intersects lines

AB

and

AD

at points

X

and

Y

, respectively. Prove that the points

P, Q, X

and

Y

lie on the same circle.