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Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Juniors 2003+ geometry
2011.8.41
<ABM =<LAC if <ANC = <ALB, medians (2011 Kyiv City MO 8.4.1)
<ABM =<LAC if <ANC = <ALB, medians (2011 Kyiv City MO 8.4.1)
Source:
July 14, 2020
geometry
equal angles
Medians
Problem Statement
The medians
A
L
,
B
M
AL, BM
A
L
,
BM
, and
C
N
CN
CN
are drawn in the triangle
A
B
C
ABC
A
BC
. Prove that
∠
A
N
C
=
∠
A
L
B
\angle ANC = \angle ALB
∠
A
NC
=
∠
A
L
B
if and only if
∠
A
B
M
=
∠
L
A
C
\angle ABM =\angle LAC
∠
A
BM
=
∠
L
A
C
.(Veklich Bogdan)
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