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National and Regional Contests
Russia Contests
Moscow Mathematical Olympiad
1956 Moscow Mathematical Olympiad
320
320
Part of
1956 Moscow Mathematical Olympiad
Problems
(1)
MMO 320 Moscow MO 1956 triangles ABC,BCD,CDA,DAB not all acute
Source:
8/19/2019
Prove that there are no four points
A
,
B
,
C
,
D
A, B, C, D
A
,
B
,
C
,
D
on a plane such that all triangles
△
A
B
C
,
△
B
C
D
,
△
C
D
A
,
△
D
A
B
\vartriangle ABC,\vartriangle BCD, \vartriangle CDA, \vartriangle DAB
△
A
BC
,
△
BC
D
,
△
C
D
A
,
△
D
A
B
are acute ones.
acute
geometry
angles