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National and Regional Contests
Germany Contests
German National Olympiad
2000 German National Olympiad
3
3
Part of
2000 German National Olympiad
Problems
(1)
<BAO, < CBO, < ACO >= 30^o, O interior of ABC => ABC equilateral
Source: Germany 2000 p3
2/23/2020
Suppose that an interior point
O
O
O
of a triangle
A
B
C
ABC
A
BC
is such that the angles
∠
B
A
O
,
∠
C
B
O
,
∠
A
C
O
\angle BAO,\angle CBO, \angle ACO
∠
B
A
O
,
∠
CBO
,
∠
A
CO
are all greater than or equal to
3
0
o
30^o
3
0
o
. Prove that the triangle
A
B
C
ABC
A
BC
is equilateral.
Equilateral
angles
geometry