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Let

C_{1}

and

C_{2}

be concentric circles, with

C_{2}

in the interior of

C_{1}

. From a point

A

C_{1}

, draw the tangent

AB

C_{2}

(B \in C_{2})

. Let

C

be the second point of intersection of

AB

and

C_{1}

,and let

D

be the midpoint of

AB

. A line passing through

A

intersects

C_{2}

E

and

F

in such a way that the perpendicular bisectors of

DE

and

CF

intersect at a point

M

AB

. Find, with proof, the ratio

AM/MC

.
This question is taken from Mathematical Olympiad Challenges , the 9-th exercise in 1.3 Power of a Point.

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