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Line passes through circumcenters is parallel to AD

Source: All russian olympiad 2016,Day1,grade 10,P2

May 1, 2016

geometrycircumcirclecyclic quadrilateralgeometry proposed

Problem Statement

Diagonals

AC,BD

of cyclic quadrilateral

ABCD

intersect at

P

.Point

Q

is on

BC

(between

B

and

C

) such that

PQ \perp AC

.Prove that the line passes through the circumcenters of triangles

APD

and

BQD

is parallel to

AD

.(A.Kuznetsov)