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Old Kyiv MO Geometry
Kyiv City MO Juniors Round2 2010+ geometry
2015.7.41
2015.7.41
Part of
Kyiv City MO Juniors Round2 2010+ geometry
Problems
(1)
DM = MB wanted, AO: OB = CO: OD = 1: 2 (2015 Kyiv City MO Round2 7.4.1)
Source:
9/3/2020
The equal segments
A
B
AB
A
B
and
C
D
CD
C
D
intersect at the point
O
O
O
and divide it by the relation
A
O
:
O
B
=
C
O
:
O
D
=
1
:
2
AO: OB = CO: OD = 1: 2
A
O
:
OB
=
CO
:
O
D
=
1
:
2
. The lines
A
D
AD
A
D
and
B
C
BC
BC
intersect at the point
M
M
M
. Prove that
D
M
=
M
B
DM = MB
D
M
=
MB
.
equal segments
geometry