2009 AIME II Problem 15

Let \overline{M N} be a diameter of a circle with diameter 1 . Let A and B be points on one of the
semicircular arcs determined by \overline{M N} such that A is the midpoint of the semicircle
and M B=\frac{3}{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{M N} with the chords
\overline{A C} and \overline{B C}. 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.