MathDB

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\equal{}\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\minus{}s\sqrt{t}, where

r

s

, and

t

are positive integers and

t

is not divisible by the square of any prime. Find r\plus{}s\plus{}t.

Problem Statement