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Caucasus Mathematical Olympiad
2021 Caucasus Mathematical Olympiad
2
A point on the median
A point on the median
Source: VI Caucasus Mathematical Olympiad
March 14, 2021
geometry
Problem Statement
In a triangle
A
B
C
ABC
A
BC
let
K
K
K
be a point on the median
B
M
BM
BM
such that
C
K
=
C
M
CK=CM
C
K
=
CM
. It appears that
∠
C
B
M
=
2
∠
A
B
M
\angle CBM = 2 \angle ABM
∠
CBM
=
2∠
A
BM
. Prove that
B
C
=
M
K
BC=MK
BC
=
M
K
.
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