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AMPK is circumscribed

Source: ARO Regional stage 2023 9.8

February 16, 2023

geometryRussia

Problem Statement

In an acute triangle

ABC

, let

M

and

N

be the midpoints of

AB

and

AC

and let

P

be its altitude from

B

. Its incircle touches

AC

at

K

and the line through

K

parallel to

MH

meets

MN

at

P

. Prove that

AMPK

has an incircle.

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