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Girls in Math at Yale 2022 Problem 12: Computationalized Oly Geo part n

Source:

February 27, 2022

Yalecollege

Problem Statement

Let

\widehat{BC}

be a triangle with

AB = 5

,

BC = 7

, and

CA = 8

, and let

D

be a point on arc

\widehat{BC}

of its circumcircle

\Omega

. Suppose that the angle bisectors of

\angle ADB

and

\angle ADC

meet

AB

and

AC

at

E

and

F

, respectively, and that

EF

and

BC

meet at

G

. Line

GD

meets

\Omega

at

T

. If the maximum possible value of

AT^2

can be expressed as

\frac{a}{b}

for positive integers

a, b

with

\gcd (a,b) = 1

, find

a + b

.
Proposed by Andrew Wu

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