MathDB

2017 Geometry Tiebreaker #2

Source:

November 19, 2022

2017Geometry Tiebreaker

Problem Statement

Circles

A,B,C

are externally tangent. Let

P

be the tangent point between circles

A

and

C

, and

Q

be the tangent point between circles

B

and

C

. Let

r_C

be the radius of circle

C

. If the chord connecting

P

and

Q

has length

r_C\sqrt{2}

and the radii of circles

A

and

B

are

4

and

7

, respectively, what is the radius of circle

C

?

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