2016 APMO Problems/Problem 3

Problem

Let $AB$ and $AC$ be two distinct rays not lying on the same line, and let $\omega$ be a circle with center $O$ that is tangent to ray $AC$ at $E$ and ray $AB$ at $F$ . Let $R$ be a point on segment $EF$ . The line through $O$ parallel to $EF$ intersects line $AB$ at $P$ . Let $N$ be the intersection of lines $PR$ and $AC$ , and let $M$ be the intersection of line $AB$ and the line through $R$ parallel to $AC$ . Prove that line $MN$ is tangent to $\omega$ .

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2016 APMO Problems/Problem 3

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