MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Girls in Math at Yale
2022 Girls in Math at Yale
12
12
Part of
2022 Girls in Math at Yale
Problems
(1)
Girls in Math at Yale 2022 Problem 12: Computationalized Oly Geo part n
Source:
2/27/2022
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
=
5
AB = 5
A
B
=
5
,
B
C
=
7
BC = 7
BC
=
7
, and
C
A
=
8
CA = 8
C
A
=
8
, and let
D
D
D
be a point on arc
B
C
^
\widehat{BC}
BC
of its circumcircle
Ω
\Omega
Ω
. Suppose that the angle bisectors of
∠
A
D
B
\angle ADB
∠
A
D
B
and
∠
A
D
C
\angle ADC
∠
A
D
C
meet
A
B
AB
A
B
and
A
C
AC
A
C
at
E
E
E
and
F
F
F
, respectively, and that
E
F
EF
EF
and
B
C
BC
BC
meet at
G
G
G
. Line
G
D
GD
G
D
meets
Ω
\Omega
Ω
at
T
T
T
. If the maximum possible value of
A
T
2
AT^2
A
T
2
can be expressed as
a
b
\frac{a}{b}
b
a
for positive integers
a
,
b
a, b
a
,
b
with
gcd
(
a
,
b
)
=
1
\gcd (a,b) = 1
g
cd
(
a
,
b
)
=
1
, find
a
+
b
a + b
a
+
b
.Proposed by Andrew Wu
Yale
college