Problems(1)
In an acute triangle ABC, the altitude from C intersects AB at E and the altitude from B intersects AC at D. CE and BD intersect at a point H. A circle with diameter DE intersects AB and AC at points F,G respectively. FG and AH intersect at K. If BC=25, BD=20, and BE=7, the length of AK is of the form qp , where p,q are relatively prime positive integers. Find p+q. geometry