Difference between revisions of "2002 AIME I Problems/Problem 11"
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== Problem == | == Problem == | ||
| + | Let <math>ABCD</math> and <math>BCFG</math> be two faces of a cube with <math>AB=12</math>. A beam of light emanates from vertex <math>A</math> and reflects off face <math>BCFG</math> at point <math>P</math>, which is 7 units from <math>\overline{BG}</math> and 5 units from <math>\overline{BC}</math>. The beam continues to be reflected off the faces of the cube. The length of the light path from the time it leaves point <math>A</math> until it next reaches a vertex of the cube is given by <math>m\sqrt{n}</math>, where <math>m</math> and <math>n</math> are integers and <math>n</math> is not divisible by the square of any prime. Find <math>m+n</math>. | ||
== Solution == | == Solution == | ||
Revision as of 17:10, 25 September 2007
Problem
Let 
and 
be two faces of a cube with 
. A beam of light emanates from vertex 
and reflects off face at point 
, which is 7 units from 
and 5 units from 
. The beam continues to be reflected off the faces of the cube. The length of the light path from the time it leaves point until it next reaches a vertex of the cube is given by 
, where 
and 
are integers and is not divisible by the square of any prime. Find 
.
Solution
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