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Three Points on a Circle

Source:

January 5, 2009
probabilitycalculusrotationgeometrytrigonometry

Problem Statement

Three points are chosen randomly and independently on a circle. What is the probability that all three pairwise distances between the points are less than the radius of the circle? <spanclass=′latex−bold′>(A)</span> 136<spanclass=′latex−bold′>(B)</span> 124<spanclass=′latex−bold′>(C)</span> 118<spanclass=′latex−bold′>(D)</span> 112<spanclass=′latex−bold′>(E)</span> 19 <span class='latex-bold'>(A)</span>\ \frac{1}{36} \qquad <span class='latex-bold'>(B)</span>\ \frac{1}{24} \qquad <span class='latex-bold'>(C)</span>\ \frac{1}{18} \qquad <span class='latex-bold'>(D)</span>\ \frac{1}{12} \qquad <span class='latex-bold'>(E)</span>\ \frac{1}{9}
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