2008 Mock ARML 2 Problems/Problem 4
Problem
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.
Solution
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,
See also
2008 Mock ARML 2 (Problems, Source) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 |