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2013 Harvard-MIT Mathematics Tournament
14
14
Part of
2013 Harvard-MIT Mathematics Tournament
Problems
(1)
2013 HMMT Guts #14: Angle Bisectors Galore
Source:
3/26/2013
Consider triangle
A
B
C
ABC
A
BC
with
∠
A
=
2
∠
B
\angle A=2\angle B
∠
A
=
2∠
B
. The angle bisectors from
A
A
A
and
C
C
C
intersect at
D
D
D
, and the angle bisector from
C
C
C
intersects
A
B
‾
\overline{AB}
A
B
at
E
E
E
. If
D
E
D
C
=
1
3
\dfrac{DE}{DC}=\dfrac13
D
C
D
E
=
3
1
, compute
A
B
A
C
\dfrac{AB}{AC}
A
C
A
B
.
HMMT
trigonometry
ratio
geometry
angle bisector