MathDB

BMT 2020 Fall - Geometry 2

Source:

December 30, 2021

geometry

Problem Statement

Let

O

be a circle with diameter

AB = 2

. Circles

O_1

and

O_2

have centers on

\overline{AB}

such that

O

is tangent to

O_1

at

A

and to

O_2

at

B

, and

O_1

and

O_2

are externally tangent to each other. The minimum possible value of the sum of the areas of

O_1

and

O_2

can be written in the form

\frac{m\pi}{n}

where

m

and

n

are relatively prime positive integers. Compute

m + n

.

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