1994 AIME Problem 14

A beam of light strikes \overline{B C} at point C with angle of incidence \alpha=19.94^{\circ} and reflects with an equal angle of reflection as shown. The light beam continues its path, reflecting off line segments \overline{A B} and \overline{B C} according to the rule: angle of incidence equals angle of reflection. Given that \beta=\alpha / 10=1.994^{\circ} and A B=B C, determine the number of times the light beam will bounce off the two line segments. Include the first reflection at C in your count.

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