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MMATHS 2021, TB Problem 4: Initially I Asked For XY^2 But I'm Dumb

Source:

October 31, 2021

YaleMMATHS

Problem Statement

Let triangle

ABC

with incenter

I

and circumcircle

\Gamma

satisfy

AB = 6\sqrt{3}, BC = 14,

and

CA = 22

. Construct points

P

and

Q

on rays

BA

and

CA

such that

BP = CQ = 14

. Lines

PI

and

QI

meet the tangents from

B

and

C

to

\Gamma

, respectively, at points

X

and

Y

. If

XY

can be expressed as

a\sqrt{b} - c

for positive integers

a,b,c

with

c

squarefree, find

a + b + c

.
Proposed by Andrew Wu

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