2003 AIME II Problems/Problem 15: Difference between revisions

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 == 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 ==

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