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1966 IMO Shortlist
36
36
Part of
1966 IMO Shortlist
Problems
(1)
Poland 6
Source: IMO LongList 1959-1966 Problem 36
9/2/2004
Let
A
B
C
D
ABCD
A
BC
D
be a quadrilateral inscribed in a circle. Show that the centroids of triangles
A
B
C
,
ABC,
A
BC
,
C
D
A
,
CDA,
C
D
A
,
B
C
D
,
BCD,
BC
D
,
D
A
B
DAB
D
A
B
lie on one circle.
geometry
complex numbers
cyclic quadrilateral
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