2003 AIME I Problem 15

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.