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Benelux Olympiad 2018, Problem 3

Source: BxMO 2018, Problem 3

April 28, 2018

BxMOBeneluxgeometry

Problem Statement

Let

ABC

be a triangle with orthocentre

H

, and let

D

,

E

, and

F

denote the respective midpoints of line segments

AB

,

AC

, and

AH

. The reflections of

B

and

C

in

QE

are

P

and

Q

, respectively. (a) Show that lines

PE

and

QD

intersect on the circumcircle of triangle

ABC

. (b) Prove that lines

PD

and

QE

intersect on line segment

AH

.

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