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Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
2001 India National Olympiad
5
5
Part of
2001 India National Olympiad
Problems
(1)
Equilateral
Source: INMO 2001 Problem 5
10/10/2005
A
B
C
ABC
A
BC
is a triangle.
M
M
M
is the midpoint of
B
C
BC
BC
.
∠
M
A
B
=
∠
C
\angle MAB = \angle C
∠
M
A
B
=
∠
C
, and
∠
M
A
C
=
1
5
∘
\angle MAC = 15^{\circ}
∠
M
A
C
=
1
5
∘
. Show that
∠
A
M
C
\angle AMC
∠
A
MC
is obtuse. If
O
O
O
is the circumcenter of
A
D
C
ADC
A
D
C
, show that
A
O
D
AOD
A
O
D
is equilateral.
geometry
circumcircle
trigonometry
trig identities
Law of Sines
geometry unsolved