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Canada National Olympiad
1993 Canada National Olympiad
3
Perpendicular Medians and Trig
Perpendicular Medians and Trig
Source: CMO 1993 Problem 3
January 25, 2007
trigonometry
symmetry
Problem Statement
In triangle
A
B
C
,
ABC,
A
BC
,
the medians to the sides
A
B
‾
\overline{AB}
A
B
and
A
C
‾
\overline{AC}
A
C
are perpendicular. Prove that
cot
B
+
cot
C
≥
2
3
.
\cot B+\cot C\ge \frac23.
cot
B
+
cot
C
≥
3
2
.
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