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PQ parallel RS

Source: Own. IMO 2022 Malaysian Training Camp 1

February 26, 2022

geometry

Problem Statement

Let

\omega

be the circumcircle of an actue triangle

ABC

and let

H

be the feet of aliitude from

A

to

BC

. Let

M

and

N

be the midpoints of the sides

AC

and

AB

. The lines

BM

and

CN

intersect each other at

G

and intersect

HQ

at

P

and

Q

respectively. The circles

(HMG)

and

(HNG)

intersect the segments

HP

and

HQ

again at

R

and

S

respectively. Prove that

PQ\parallel RS

.

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