2009 AIME II Problems/Problem 15

Let $\overline{MN}$ be a diameter of a circle with diameter 1. Let $A$ and $B$ be points on one of the semicircular arcs determined by $\overline{MN}$ such that $A$ is the midpoint of the semicircle and $MB= {3}over{5}$ . Point $C$ lies on the other semicircular arc. Let $d$ be the length of the line segment whose endpoints are the intersections of diameter $\overline{MN}$ with chords $\overline{AC}$ and $\overline{BC}$ . The largest possible value of $d$ can be written in the form r-s*sqrt (t), where r, s, and t are positive integers and t is not divisible by the square of any prime. Find r+s+t.

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2009 AIME II Problems/Problem 15