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April 26, 2022

Problem Statement

Let

\Gamma_1

be a circle with radius

\frac{5}{2}

.

A

,

B

, and

C

are points on

\Gamma_1

such that

\overline{AB} = 3

and

\overline{AC} = 5

. Let

\Gamma_2

be a circle such that

\Gamma_2

is tangent to

AB

and

BC

at

Q

and

R

, and

\Gamma_2

is also internally tangent to

\Gamma_1

at

P

.

\Gamma_2

intersects

AC

at

X

and

Y

.

[PXY]

can be expressed as

\frac{a\sqrt{b}}{c}

. Find

a+b+c

.
2022 CCA Math Bonanza Individual Round #5

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