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Lots of Tangency

Source: 2014 AIME II Problem #8

March 27, 2014

LaTeXtrigonometryAsymptotegeometrygeometric transformationreflectionPythagorean Theorem

Problem Statement

Circle

C

with radius

2

has diameter

\overline{AB}

. Circle

D

is internally tangent to circle

C

at

A

. Circle

E

is internally tangent to circle

C,

externally tangent to circle

D,

and tangent to

\overline{AB}

. The radius of circle

D

is three times the radius of circle

E

and can be written in the form

\sqrt{m} - n,

where

m

and

n

are positive integers. Find

m+n

.

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