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Problem 5 of First round

Source: XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade

September 9, 2022

geometry

Problem Statement

Let

\Delta ABC

be an acute scalene triangle with

AC<BC

, an orthocenter

H

and altitudes

AE

,

BF

. The points

E'

and

F'

are symmetrical to

E

and

F

with respect to

A

and

B

respectively. Point

O

is the center of the circumscribed circle of

ABC

and

M

is the midpoint of

AB

. Let

N

be the midpoint of

OM

. Prove that the tangent through

H

to the circumscribed circle of

\Delta E'HF'

is perpendicular to line

CN

.

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