MathDB

2021 Geo #2: Recursive Area

Source:

May 30, 2021

geometry

Problem Statement

Let

X_0

be the interior of a triangle with side lengths

3, 4,

and

5

. For all positive integers

n

, define

X_{21}

to be the set of points within

1

unit of some point in

X_{n-1}

. The area of the region outside

X_{20}

but inside

X_{21}

can be written as

a\pi + b

, for integers

a

and

b

. Compute

100a + b

.

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