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Beautiful geometry from Kyiv MO

Source: Kyiv City MO 2024 Round 2, Problem 9.4

February 4, 2024

geometry

Problem Statement

Let

BD

be an altitude of

\triangle ABC

with

AB < BC

and

\angle B > 90^\circ

. Let

M

be the midpoint of

AC

, and point

K

be symmetric to point

D

with respect to point

M

. A perpendicular drawn from point

M

to the line

BC

intersects line

AB

at point

L

. Prove that

\angle MBL = \angle MKL

.
Proposed by Oleksandra Yakovenko

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