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MathLinks Contest 1st
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0162 geometry 1st edition Round 6 p2
0162 geometry 1st edition Round 6 p2
Source:
May 9, 2021
geometry
1st edition
Problem Statement
Given is a triangle
A
B
C
ABC
A
BC
and on its sides the triangles
A
B
M
,
B
C
N
ABM, BCN
A
BM
,
BCN
and
C
A
P
CAP
C
A
P
are build such that
∠
A
M
B
=
15
0
o
\angle AMB = 150^o
∠
A
MB
=
15
0
o
,
A
M
=
M
B
AM = MB
A
M
=
MB
,
∠
C
A
P
=
∠
C
B
N
=
3
0
o
\angle CAP = \angle CBN = 30^o
∠
C
A
P
=
∠
CBN
=
3
0
o
,
∠
A
C
P
=
∠
B
C
N
=
4
5
o
\angle ACP = \angle BCN = 45^o
∠
A
CP
=
∠
BCN
=
4
5
o
. Prove that the triangle
M
N
P
MNP
MNP
is an equilateral triangle.
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