MathDB

Median geo

Source: St. Petersburg 2023 9.3

August 12, 2023

geometry

Problem Statement

Let

M

be the midpoint of

AC

in an acute triangle

ABC

. Let

K

be a point on the minor arc

AC

, such that

\angle AKM=90^{o}

. Let

BK \cap AM=X

and the

A

-altitude meets

BM

at

Y

. Show that

XY \parallel AB

.

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