MathDB
AHSME 1950- part 3

Source:

July 20, 2008
geometry

Problem Statement

A point is selected at random inside an equilateral triangle. From this point perpendiculars are dropped to each side. The sum of these perpendiculars is:
<spanclass=latexbold>(A)</span> Least when the point is the center of gravity of the triangle<spanclass=latexbold>(B)</span> Greater than the altitude of the triangle<spanclass=latexbold>(C)</span> Equal to the altitude of the triangle<spanclass=latexbold>(D)</span> One-half the sum of the sides of the triangle<spanclass=latexbold>(E)</span> Greatest when the point is the center of gravity<span class='latex-bold'>(A)</span>\ \text{Least when the point is the center of gravity of the triangle}\qquad\\ <span class='latex-bold'>(B)</span>\ \text{Greater than the altitude of the triangle} \qquad\\ <span class='latex-bold'>(C)</span>\ \text{Equal to the altitude of the triangle}\qquad\\ <span class='latex-bold'>(D)</span>\ \text{One-half the sum of the sides of the triangle} \qquad\\ <span class='latex-bold'>(E)</span>\ \text{Greatest when the point is the center of gravity}