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K lies on the line BM

Source: 42nd International Tournament of Towns, Senior O-Level P5, Spring 2021

February 18, 2023

geometryTournament of Towns

Problem Statement

Let

O{}

be the circumcenter of an acute triangle

ABC

. Let

M{}

be the midpoint of

AC

. The straight line

BO

intersects the altitudes

AA_1{}

and

CC_1{}

at the points

H_a

and

H_c

respectively. The circumcircles of the triangles

BH_aA

and

BH_cC

have a second point of intersection

K{}

. Prove that

K{}

lies on the straight line

BM

.
Mikhail Evdokimov

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