{"status": "success", "data": {"description_md": "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.

$\\includegraphics[width=209, height=112, totalheight=112]{https://latex.artofproblemsolving.com/4/2/2/4225d4d533a980415c8bed93bb2272075aabbf01.png}$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "1994 AIME Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/94_aime_p15", "prev": "/problem/94_aime_p13"}}