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Problems
Contests
National and Regional Contests
Serbia Contests
Serbia Team Selection Test
2005 Serbia Team Selection Test
4
4
Part of
2005 Serbia Team Selection Test
Problems
(1)
angle inequality involving centroid of triangle
Source: Serbia & Montenegro TST 2005 problem 4
6/1/2005
Let
T
T
T
be the centroid of triangle
A
B
C
ABC
A
BC
. Prove that
1
sin
∠
T
A
C
+
1
sin
∠
T
B
C
≥
4
\frac 1{\sin \angle TAC} + \frac 1{\sin \angle TBC} \geq 4
sin
∠
T
A
C
1
+
sin
∠
TBC
1
≥
4
inequalities
trigonometry
geometry proposed
geometry