MathDB

2021 Geo Div 1 P5

Source:

March 2, 2021

geometry

Problem Statement

Let

\gamma_1, \gamma_2, \gamma_3

be three circles with radii

3, 4, 9,

respectively, such that

\gamma_1

and

\gamma_2

are externally tangent at

C,

and

\gamma_3

is internally tangent to

\gamma_1

and

\gamma_2

at

A

and

B,

respectively. Suppose the tangents to

\gamma_3

at

A

and

B

intersect at

X.

The line through

X

and

C

intersect

\gamma_3

at two points,

P

and

Q.

Compute the length of

PQ.

Proposed by Kyle Lee

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