Difference between revisions of "1994 AIME Problems/Problem 14"

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== See also ==
 
== See also ==
 
{{AIME box|year=1994|num-b=13|num-a=15}}
 
{{AIME box|year=1994|num-b=13|num-a=15}}
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[[Category:Intermediate Geometry Problems]]

Revision as of 18:01, 4 December 2007

Problem

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.

AIME 1994 Problem 14.png

Solution

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See also

1994 AIME (ProblemsAnswer KeyResources)
Preceded by
Problem 13
Followed by
Problem 15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions