AHSME 1950 Problem 48

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: $\textbf{(A)}\ \text{Least when the point is the center of gravity of the triangle} \\ \textbf{(B)}\ \text{Greater than the altitude of the triangle} \\ \textbf{(C)}\ \text{Equal to the altitude of the triangle} \\ \textbf{(D)}\ \text{One-half the sum of the sides of the triangle} \\ \textbf{(E)}\ \text{Greatest when the point is the center of gravity}$