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One on quads

Source: Indian IMOTC 2005 Day 4 Problem 1

September 23, 2005

geometryindia

Problem Statement

Let

ABCD

be a convex quadrilateral. The lines parallel to

AD

and

CD

through the orthocentre

H

of

ABC

intersect

AB

and

BC

Crespectively at

P

and

Q

. prove that the perpendicular through

H

to th eline

PQ

passes through th eorthocentre of triangle

ACD

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