Difference between revisions of "2003 AIME I Problems/Problem 15"

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== See also ==
 
== See also ==
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* [[2003 AIME I Problems/Problem 14 | Previous problem]]
 
* [[2003 AIME I Problems]]
 
* [[2003 AIME I Problems]]

Revision as of 18:44, 4 November 2006

Problem

In $\triangle ABC, AB = 360, BC = 507,$ and $CA = 780.$ Let $M$ be the midpoint of $\overline{CA},$ and let $D$ be the point on $\overline{CA}$ such that $\overline{BD}$ bisects angle $ABC.$ Let $F$ be the point on $\overline{BC}$ such that $\overline{DF} \perp \overline{BD}.$ Suppose that $\overline{DF}$ meets $\overline{BM}$ at $E.$ The ratio $DE: EF$ can be written in the form $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$

Solution

See also

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