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Swedish Mathematical Competition
2005 Swedish Mathematical Competition
3
3
Part of
2005 Swedish Mathematical Competition
Problems
(1)
Angle Bisectors
Source: 2005 Swedish Mathematical Competition #3
1/6/2018
In a triangle
A
B
C
ABC
A
BC
the bisectors of angles
A
A
A
and
C
C
C
meet the opposite sides at
D
D
D
and
E
E
E
respectively. Show that if the angle at
B
B
B
is greater than
6
0
ā
60^\circ
6
0
ā
, then
A
E
+
C
D
<
A
C
AE +CD <AC
A
E
+
C
D
<
A
C
.
Sweden
geometry
angle bisector