MathDB

Convex quadrilateral

Source: HOMC 2008

March 8, 2016

geometryhomc

Problem Statement

Consider a convex quadrilateral

ABCD

. Let

O

be the intersection of

AC

and

BD

;

M, N

be the centroid of

MN\bot PQ

and

\Delta COD

and

P, Q

be orthocenter of

\Delta BOC

and

\Delta DOA

, respectively. Prove that

MN\bot PQ

.

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