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Prove that 4 points lie on a circumference

Source: Iberoamerican Olympiad 2014, Problem 5

September 24, 2014

geometrygeometric transformationreflectiontrapezoidcircumcirclecyclic quadrilateralgeometry unsolved

Problem Statement

Let

ABC

be an acute triangle and

H

its orthocenter. Let

D

be the intersection of the altitude from

A

to

BC

. Let

M

and

X

be the midpoints of

Y

and

CH

, respectively. Let the lines

DM

and

DN

intersect

AB

and

AC

at points

X

and

Y

respectively. If

P

is the intersection of

XY

with

BH

and

Q

the intersection of

XY

with

CH

, show that

H, P, D, Q

lie on a circumference.

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