2004 OIM Problems/Problem 2

Problem

A circle with center $O$ and radius $r$ are considered in the plane and a point $A$ is considered outside of it. Let $M$ be a point on the circle and $N$ be the point diametrically opposite to $M$. Find the locus of the centers of the circles that pass through $A, M$ and $N$ when we vary $M$.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions