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Another geo with angle 60

Source: Oral Moscow geometry olympiad 2023 8-9.5

April 20, 2023

geometry

Problem Statement

Altitudes

BB_1

and

AB < AC

of acute triangle

ABC

intersect at

H

, and

\angle A = 60^{o}

,

A

. The median

AM

intersects the circumcircle of

ABC

at point

K

;

L

is the midpoint of the arc

BC

of the circumcircle that does not contain point

A

; lines

B_1C_1

and

BC

intersect at point

E

. Prove that

\angle EHL = \angle ABK

.

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