MathDB

Five lighthouses are located, in order, at points

A, B, C, D

, and

E

along the shore of a circular lake with a diameter of

10

miles. Segments

AD

and

BE

are diameters of the circle. At night, when sitting at

A

, the lights from

B, C, D

, and

E

appear to be equally spaced along the horizon. The perimeter in miles of pentagon

ABCDE

can be written

m +\sqrt{n}

, where

m

and

n

are positive integers. Find

m + n

Problem Statement