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Consecutive Vertices and the Side Opposite

Source: AHSME 1963 Problem 10

January 9, 2014
geometrycircumcircleperpendicular bisectorPythagorean TheoremAMC

Problem Statement

Point PP is taken interior to a square with side-length aa and such that is it equally distant from two consecutive vertices and from the side opposite these vertices. If dd represents the common distance, then dd equals:
<spanclass=′latex−bold′>(A)</span> 3a5<spanclass=′latex−bold′>(B)</span> 5a8<spanclass=′latex−bold′>(C)</span> 3a8<spanclass=′latex−bold′>(D)</span> a22<spanclass=′latex−bold′>(E)</span> a2<span class='latex-bold'>(A)</span>\ \dfrac{3a}{5} \qquad <span class='latex-bold'>(B)</span>\ \dfrac{5a}{8} \qquad <span class='latex-bold'>(C)</span>\ \dfrac{3a}{8} \qquad <span class='latex-bold'>(D)</span>\ \dfrac{a\sqrt{2}}{2} \qquad <span class='latex-bold'>(E)</span>\ \dfrac{a}{2}
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