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2013 HMMT Guts #16: Rolling a Ball out of Boredom

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March 26, 2013
HMMTgeometrygeometric transformationreflectionPythagorean Theorem

Problem Statement

The walls of a room are in the shape of a triangle ABCABC with ∠ABC=90∘\angle ABC = 90^\circ, ∠BAC=60∘\angle BAC = 60^\circ, and AB=6AB=6. Chong stands at the midpoint of BCBC and rolls a ball toward ABAB. Suppose that the ball bounces off ABAB, then ACAC, then returns exactly to Chong. Find the length of the path of the ball.
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