Henry Ernest Dudeney/Puzzles and Curious Problems/328 - Choosing a Site/Solution

by : $328$

 * Choosing a Site

Solution
Anywhere he likes.

Proof
Let perpendiculars be drawn to the sides of an equilateral triangle from any point within it.

Then from Viviani's Theorem, the sum of their lengths is equal to the height of that equilateral triangle.

So, from whatever point you choose inside this equilateral triangle, the sum of those lengths is the same.