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Vietnam Contests
Hanoi Open Mathematics Competition
2008 Hanoi Open Mathematics Competitions
9
9
Part of
2008 Hanoi Open Mathematics Competitions
Problems
(1)
find point, equal angles, parallelogram related (HOMC 2008 Q9)
Source:
7/25/2019
Consider a triangle
A
B
C
ABC
A
BC
. For every point M
∈
B
C
\in BC
∈
BC
,we define
N
∈
C
A
N \in CA
N
∈
C
A
and
P
∈
A
B
P \in AB
P
∈
A
B
such that
A
P
M
N
APMN
A
PMN
is a parallelogram. Let
O
O
O
be the intersection of
B
N
BN
BN
and
C
P
CP
CP
. Find
M
∈
B
C
M \in BC
M
∈
BC
such that
∠
P
M
O
=
∠
O
M
N
\angle PMO=\angle OMN
∠
PMO
=
∠
OMN
geometry
parallelogram
equal angles
construction