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 $$a+b+c.$$

(第二十二届AIME1 2004 第14题)