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International Contests
Tournament Of Towns
1993 Tournament Of Towns
(380) 2
(380) 2
Part of
1993 Tournament Of Towns
Problems
(1)
TOT 380 1993 Autumn O J2 collinear midpoints
Source:
6/12/2024
Vertices
A
A
A
,
B
B
B
and
C
C
C
of a triangle are connected with points
A
′
A'
A
′
,
B
′
B'
B
′
and
C
′
C'
C
′
lying in the opposite sides of the triangle (not at vertices). Can the midpoints of the segments
A
A
′
AA'
A
A
′
,
B
B
′
BB'
B
B
′
and
C
C
′
CC'
C
C
′
lie in a straight line?(Folklore)
geometry
collinear