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Old Kyiv MO Geometry
Kyiv City MO Juniors Round2 2010+ geometry
2019.8.4
2019.8.4
Part of
Kyiv City MO Juniors Round2 2010+ geometry
Problems
(1)
angle wanted, 75-60-45 triangle, BC=CT (2019 Kyiv City MO Round2 8.4)
Source:
9/17/2020
In the triangle
A
B
C
ABC
A
BC
it is known that
∠
A
=
7
5
o
,
∠
C
=
4
5
o
\angle A = 75^o, \angle C = 45^o
∠
A
=
7
5
o
,
∠
C
=
4
5
o
. On the ray
B
C
BC
BC
beyond the point
C
C
C
the point
T
T
T
is taken so that
B
C
=
C
T
BC = CT
BC
=
CT
. Let
M
M
M
be the midpoint of the segment
A
T
AT
A
T
. Find the measure of the
∠
B
M
C
\angle BMC
∠
BMC
.(Anton Trygub)
geometry
angles
equal segments