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National and Regional Contests
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Official Ukraine Selection Cycle
Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Juniors 2003+ geometry
2021.8.41
2021.8.41
Part of
Kyiv City MO Juniors 2003+ geometry
Problems
(1)
AM=KB wanted, AK =AO, KM =MC , KM //AC (2021 Kyiv City MO 8.4.1)
Source:
2/16/2021
On the sides
A
B
AB
A
B
and
B
C
BC
BC
of the triangle
A
B
C
ABC
A
BC
, the points
K
K
K
and
M
M
M
are chosen so that
K
M
∥
A
C
KM \parallel AC
K
M
∥
A
C
. The segments
A
M
AM
A
M
and
K
C
KC
K
C
intersect at the point
O
O
O
. It is known that
A
K
=
A
O
AK =AO
A
K
=
A
O
and
K
M
=
M
C
KM =MC
K
M
=
MC
. Prove that
A
M
=
K
B
AM=KB
A
M
=
K
B
.
geometry
equal segments