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)