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2014 Harvard-MIT Mathematics Tournament
19
19
Part of
2014 Harvard-MIT Mathematics Tournament
Problems
(1)
2014 Guts #19: Bisectors in a Trapezoid
Source:
4/21/2014
Let
A
B
C
D
ABCD
A
BC
D
be a trapezoid with
A
B
∥
C
D
AB\parallel CD
A
B
∥
C
D
. The bisectors of
∠
C
D
A
\angle CDA
∠
C
D
A
and
∠
D
A
B
\angle DAB
∠
D
A
B
meet at
E
E
E
, the bisectors of
∠
A
B
C
\angle ABC
∠
A
BC
and
∠
B
C
D
\angle BCD
∠
BC
D
meet at
F
F
F
, the bisectors of
∠
B
C
D
\angle BCD
∠
BC
D
and
∠
C
D
A
\angle CDA
∠
C
D
A
meet at
G
G
G
, and the bisectors of
∠
D
A
B
\angle DAB
∠
D
A
B
and
∠
A
B
C
\angle ABC
∠
A
BC
meet at
H
H
H
. Quadrilaterals
E
A
B
F
EABF
E
A
BF
and
E
D
C
F
EDCF
E
D
CF
have areas
24
24
24
and
36
36
36
, respectively, and triangle
A
B
H
ABH
A
B
H
has area
25
25
25
. Find the area of triangle
C
D
G
CDG
C
D
G
.
geometry
trapezoid