MathDB

A unicorn is tethered by a 20-foot silver rope to the base of a magician's cylindrical tower whose radius is 8 feet. The rope is attached to the tower at ground level and to the unicorn at a height of 4 feet. The unicorn has pulled the rope taut, the end of the rope is 4 feet from the nearest point on the tower, and the length of the rope that is touching the tower is

\frac{a-\sqrt{b}}c

feet, where

a, b,

and

c

are positive integers, and

c

is prime. Find

a+b+c

Problem Statement