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Problem Description 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 \( MB=\frac35\). 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 the 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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