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IMO Shortlist
1971 IMO Shortlist
12
12
Part of
1971 IMO Shortlist
Problems
(1)
The midpoints either are collinear or form equilateral trgle
Source:
9/22/2010
Two congruent equilateral triangles
A
B
C
ABC
A
BC
and
A
′
B
′
C
′
A'B'C'
A
′
B
′
C
′
in the plane are given. Show that the midpoints of the segments
A
A
′
,
B
B
′
,
C
C
′
AA',BB', CC'
A
A
′
,
B
B
′
,
C
C
′
either are collinear or form an equilateral triangle.
geometry
congruent triangles
midpoints
collinear
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