1998 USAMO Problems/Problem 2

Problem

Let ${\cal C}_1$ and ${\cal C}_2$ be concentric circles, with ${\cal C}_2$ in the interior of ${\cal C}_1$ . From a point $A$ on ${\cal C}_1$ one draws the tangent $AB$ to ${\cal C}_2$ ( $B\in {\cal C}_2$ ). Let $C$ be the second point of intersection of $AB$ and ${\cal C}_1$ , and let $D$ be the midpoint of $AB$ . A line passing through $A$ intersects ${\cal C}_2$ at $E$ and $F$ in such a way that the perpendicular bisectors of $DE$ and $CF$ intersect at a point $M$ on $AB$ . Find, with proof, the ratio $AM/MC$ .

Solution

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1998 USAMO (Problems • Resources)
Preceded by Problem 1	Followed by Problem 3
1 • 2 • 3 • 4 • 5 • 6
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1998 USAMO Problems/Problem 2

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