GeekDad Puzzle of the Week: Bermuda! Triangles! Eccentrics! Oh My! — Solution

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Photo:NASA (public domain)Photo:NASA (public domain)

Photo:NASA (public domain)

Last week, an eccentric billionaire needed your help deciding where to place his mansion on his new island. Congratulations to Marcelo who was one of several who sent in the correct answer and was chosen randomly to receive a $50 gift certificate from ThinkGeek! The rest of you may read to the end of the puzzle for a code to get $10 off a $40 or more purchase.

Puzzle

Mr. Lion has purchased a large island in the Bermuda Triangle. Being an eccentric geek, he is having the island shape changed from a rough triangle to a perfect equilateral triangle. He will have three ports built, one somewhere on each of the sides of the triangle. He wants to save money on building roads so has this question: where should he build his mansion, somewhere on the interior of the island, such that the total length of road is minimized. There must be one road from the mansion to each of the ports, and the road must be made perpendicular to its side of the island. The location of the ports is flexible insofar as there must be one on each side.

Marcelo’s answer

Given those constrains, he can put the mansion anywhere he wants, as
the total road length is going to be constant, following Viviani’s
theorem: the sum of distances from a point to the side lines of an
equilateral triangle does not depend on the point, and corresponds to
the triangle’s height.

Thanks for participating! Come back on Monday for a new puzzle. Your code for the discount at ThinkGeek is GEEKPUZZLER.

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