A beam of light strikes \(\overline{BC}\,\) 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 \(\overline{AB}\,\) and \(\overline{BC}\,\) according to the rule: angle of incidence equals angle of reflection. Given that \(\beta=\alpha/10=1.994^\circ\,\) and \(AB=AC,\,\) determine the number of times the light beam will bounce off the two line segments. Include the first reflection at \(C\,\) in your count.

(第十二届AIME1994 第14题)