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IMO Longlists
1985 IMO Longlists
73
73
Part of
1985 IMO Longlists
Problems
(1)
Prove that the segments are proportional
Source:
9/14/2010
Let
A
1
A
2
,
B
1
B
2
,
C
1
C
2
A_1A_2,B_1B_2, C_1C_2
A
1
A
2
,
B
1
B
2
,
C
1
C
2
be three equal segments on the three sides of an equilateral triangle. Prove that in the triangle formed by the lines
B
2
C
1
,
C
2
A
1
,
A
2
B
1
B_2C_1, C_2A_1,A_2B_1
B
2
C
1
,
C
2
A
1
,
A
2
B
1
, the segments
B
2
C
1
,
C
2
A
1
,
A
2
B
1
B_2C_1, C_2A_1,A_2B_1
B
2
C
1
,
C
2
A
1
,
A
2
B
1
are proportional to the sides in which they are contained.
geometry