2015 AIME II Problem 11

The circumcircle of acute \triangle ABC has center O. The line passing through point O perpendicular to \overline{OB} intersects lines AB and BC at P and Q, respectively. Also AB=5, BC=4, BQ=4.5, and BP=\frac{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.