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Geo Geo Geo

Source: 2023 AIME II / 9

February 16, 2023

AMCAIMEAIME II

Problem Statement

Circles

\omega_1

and

\omega_2

intersect at two points

P

and

Q

, and their common tangent line closer to

P

intersects

\omega_1

and

\omega_2

at points

A

and

B

, respectively. The line parallel to line

AB

that passes through

P

intersects

\omega_1

and

\omega_2

for the second time at points

X

and

Y

, respectively. Suppose

PX = 10, PY = 14,

and

PQ = 5

. Then the area of trapezoid

XABY

is

m\sqrt{n}

where

m

and

n

are positive integers and

n

is not divisible by the square of any prime. Find

m + n

.

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