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Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Juniors 2003+ geometry
2019.8.3
2019.8.3
Part of
Kyiv City MO Juniors 2003+ geometry
Problems
(1)
<B= 30^o wanted, 2AC=AB,< A = 2<B, CL = ML (2019 Kyiv City MO 8.3)
Source:
9/16/2020
In the triangle
A
B
C
ABC
A
BC
it is known that
2
A
C
=
A
B
2AC=AB
2
A
C
=
A
B
and
∠
A
=
2
∠
B
\angle A = 2\angle B
∠
A
=
2∠
B
. In this triangle draw the angle bisector
A
L
AL
A
L
, and mark point
M
M
M
, the midpoint of the side
A
B
AB
A
B
. It turned out that
C
L
=
M
L
CL = ML
C
L
=
M
L
. Prove that
∠
B
=
3
0
o
\angle B= 30^o
∠
B
=
3
0
o
.(Hilko Danilo)
geometry
equal angles
angles
equal segments