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Cute Polish geo with weird orthocenter

Source: Polish MO 2nd round 2023/5

February 11, 2023

geometry

Problem Statement

Given is a triangle

ABC

with

AB>AC

. Its incircle touches

AB, AC

at

DE

, respectively. Let

CD

meet the incircle at

K

and

L

is the foot of the perpendicular from

A

to

CK

. If

M

is the midpoint of

DE

and

H

is the orthocenter of

\triangle KML

, prove that

\angle AHK=90^{o}

.
Proposed by Dominik Burek

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