Trapezoid ABCD has parallel sides AB and CD, of lengths 8 and 16, respectively. Diagonals AC and BD intersect at E, and the length of AC is 15. Find the lengths of AE and EC.

a) AE = 5, EC = 10
b) AE = 10, EC = 5
c) AE = 6, EC = 9
d) AE = 9, EC = 6