2011 AIME I Problems/Problem 14
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Let be a regular octagon. Let be the midpoints of sides , and , respectively. For , ray is suspended such that . Pairs of rays and , and , and , and and meet at , respectively. If , then $\cos{2\angle{A_{3}M_{3}B_{1}}$ (Error compiling LaTeX. Unknown error_msg) can be written as , where and are positive integers. Find .