There is a point D on side A C of acute triangle \triangle A B C. Let A M be the median drawn from A (so M is on B C ) and C H be the altitude drawn from C (so H is on A B ). Let I be the intersection of A M and C H, and let K be the intersection of A M and line segment B D. We know that A K=8, B K=8, and M K=6. Find the length of A I.