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Official Ukraine Selection Cycle
Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Juniors 2003+ geometry
2021.8.4
2021.8.4
Part of
Kyiv City MO Juniors 2003+ geometry
Problems
(1)
<ABM=<MBP wanted, AB //PC , PM_|_BM , median (2021 Kyiv City MO 8.4)
Source:
2/16/2021
Let
B
M
BM
BM
be the median of the triangle
A
B
C
ABC
A
BC
, in which
A
B
>
B
C
AB> BC
A
B
>
BC
. 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
.(Mikhail Standenko)
geometry
equal angles
angles