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Adygea Teachers' Geometry Olympiad
2022 Adygea Teachers' Geometry Olympiad
1
1
Part of
2022 Adygea Teachers' Geometry Olympiad
Problems
(1)
MN/AB =? 60-45-75 triangle (2022 Adygea Teachers' Geometry Olympiad p1)
Source:
2/28/2024
In triangle
A
B
C
ABC
A
BC
,
∠
A
=
6
0
o
\angle A = 60^o
∠
A
=
6
0
o
,
∠
B
=
4
5
o
\angle B = 45^o
∠
B
=
4
5
o
. On the sides
A
C
AC
A
C
and
B
C
BC
BC
points
M
M
M
and
N
N
N
are taken, respectively, so that the straight line
M
N
MN
MN
cuts off a triangle similar to this one. Find the ratio of
M
N
MN
MN
to
A
B
AB
A
B
if it is known that
C
M
:
A
M
=
2
:
1
CM : AM = 2:1
CM
:
A
M
=
2
:
1
.
geometry