1950 AHSME Problems/Problem 48

Problem

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:

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

Solution

By Viviani's Theorem, the answer must be $\textbf{(C)}$

1950 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 47	Followed by Problem 49
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1950 AHSME Problems/Problem 48

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