2008 Mock ARML 2 Problems/Problem 4
Equilateral triangle has a side length of . A ball begins at vertex , rolls through the interior of the triangle, bounces off side , and settles at point . Given that and , find the total distance that the ball travels.
Reflect across to point ; since the ball travels in a straight path, it follows that the distance the ball traveled is . By symmetry, . By the Law of Cosines on ,
Since , it follows that quadrilateral is a cyclic quadrilateral. By Ptolemy's Theorem,
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