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Two chords intersection

Source: 2011 AMC A Problem 20

June 25, 2011
probabilitygeometryperimeterAMC

Problem Statement

Two points on the circumference of a circle of radius r are selected independently and at random. From each point a chord of length r is drawn in a clockwise direction. What is the probability that the two chords intersect?
<spanclass=′latex−bold′>(A)</span> 16<spanclass=′latex−bold′>(B)</span> 15<spanclass=′latex−bold′>(C)</span> 14<spanclass=′latex−bold′>(D)</span> 13<spanclass=′latex−bold′>(E)</span> 12 <span class='latex-bold'>(A)</span>\ \frac{1}{6}\qquad<span class='latex-bold'>(B)</span>\ \frac{1}{5}\qquad<span class='latex-bold'>(C)</span>\ \frac{1}{4}\qquad<span class='latex-bold'>(D)</span>\ \frac{1}{3}\qquad<span class='latex-bold'>(E)</span>\ \frac{1}{2}
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