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Problems
Contests
National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Juniors 2003+ geometry
2014.851
2014.851
Part of
Kyiv City MO Juniors 2003+ geometry
Problems
(1)
MF: BK wanted, AK = AF, median related (2014 Kyiv City MO 8.5.1)
Source:
8/5/2020
On the side
A
B
AB
A
B
of the triangle
A
B
C
ABC
A
BC
mark the point
K
K
K
. The segment
C
K
CK
C
K
intersects the median
A
M
AM
A
M
at the point
F
F
F
. It is known that
A
K
=
A
F
AK = AF
A
K
=
A
F
. Find the ratio
M
F
:
B
K
MF: BK
MF
:
B
K
.
geometry
ratio
median
equal segments