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Putnam 1996 A2

Source:

June 4, 2014

Putnamcollege contests

Problem Statement

Let

\mathcal{C}_1

and

\mathcal{C}_2

be circles whose centers are

10

units apart, and whose radii are

1

and

3

. Find, with proof, the locus of all points

M

for which there exists points

X\in \mathcal{C}_1,Y\in \mathcal{C}_2

such that

M

is the midpoint of

XY

.

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