MathDB

JBMO Shortlist 2022 G5

Source: JBMO Shortlist 2022

June 26, 2023

geometryorthocenterJuniorBalkanshortlist

Problem Statement

Given is an acute angled triangle

ABC

with orthocenter

H

and circumcircle

k

. Let

\omega

be the circle with diameter

AH

and

P

be the point of intersection of

\omega

and

k

other than

A

. Assume that

BP

and

CP

intersect

\omega

for the second time at points

Q

and

R

, respectively. If

D

is the foot of the altitude from

A

to

BC

and

S

is the point of the intersection of

\omega

and

QD

, prove that

HR = HS

.

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