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Problems
Contests
National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Kyiv City MO
2021 Kyiv City MO
2021 Kyiv City MO Round 1
8.4
8.4
Part of
2021 Kyiv City MO Round 1
Problems
(1)
Return of the geo king
Source: Kyiv City MO 2021 Round 1, Problem 8.4
12/21/2023
Let
B
M
BM
BM
be the median of the triangle
A
B
C
ABC
A
BC
with
A
B
>
B
C
AB > BC
A
B
>
BC
. The point
P
P
P
is chosen so that
A
B
∥
P
C
AB\parallel PC
A
B
∥
PC
and
P
M
⊥
B
M
PM \perp BM
PM
⊥
BM
. Prove that
∠
A
B
M
=
∠
M
B
P
\angle ABM = \angle MBP
∠
A
BM
=
∠
MBP
.Proposed by Mykhailo Shandenko
geometry