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2014 Stanford Mathematics Tournament
10
10
Part of
2014 Stanford Mathematics Tournament
Problems
(1)
SMT RMT 2014 Geometry #10
Source:
10/28/2022
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
=
12
AB = 12
A
B
=
12
,
B
C
=
5
BC = 5
BC
=
5
,
A
C
=
13
AC = 13
A
C
=
13
. Let
D
D
D
and
E
E
E
be the feet of the internal and external angle bisectors from
B
B
B
, respectively. (The external angle bisector from
B
B
B
bisects the angle between
B
C
BC
BC
and the extension of
A
B
AB
A
B
.) Let
ω
\omega
ω
be the circumcircle of
△
B
D
E
\vartriangle BDE
△
B
D
E
, extend
A
B
AB
A
B
so that it intersects
ω
\omega
ω
again at
F
F
F
. Extend
F
C
F C
FC
to meet
ω
\omega
ω
again at
X
X
X
, and extend
A
X
AX
A
X
to meet
ω
\omega
ω
again at
G
G
G
. Find
F
G
F G
FG
.
geometry