Difference between revisions of "2003 AIME I Problems/Problem 15"
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== Problem == | == Problem == | ||
| + | In <math> \triangle ABC, AB = 360, BC = 507, </math> and <math> CA = 780. </math> Let <math> M </math> be the midpoint of <math> \overline{CA}, </math> and let <math> D </math> be the point on <math> \overline{CA} </math> such that <math> \overline{BD} </math> bisects angle <math> ABC. </math> Let <math> F </math> be the point on <math> \overline{BC} </math> such that <math> \overline{DF} \perp \overline{BD}. </math> Suppose that <math> \overline{DF} </math> meets <math> \overline{BM} </math> at <math> E. </math> The ratio <math> DE: EF </math> can be written in the form <math> m/n, </math> where <math> m </math> and <math> n </math> are relatively prime positive integers. Find <math> m + n. </math> | ||
== Solution == | == Solution == | ||
Revision as of 19:11, 6 August 2006
Problem
In 
and 
Let 
be the midpoint of 
and let 
be the point on 
such that 
bisects angle 
Let 
be the point on 
such that 
Suppose that 
meets 
at 
The ratio 
can be written in the form 
where 
and 
are relatively prime positive integers. Find 
