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Canada National Olympiad
1969 Canada National Olympiad
5
5
Part of
1969 Canada National Olympiad
Problems
(1)
Angle bisector
Source: Canada 1969, Problem 5
5/14/2006
Let
A
B
C
ABC
A
BC
be a triangle with sides of length
a
a
a
,
b
b
b
and
c
c
c
. Let the bisector of the angle
C
C
C
cut
A
B
AB
A
B
in
D
D
D
. Prove that the length of
C
D
CD
C
D
is
2
a
b
cos
C
2
a
+
b
.
\frac{2ab\cos \frac{C}{2}}{a+b}.
a
+
b
2
ab
cos
2
C
.
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angle bisector