1998 AHSME Problem 28

In triangle ABC, angle C is a right angle and CB > CA. Point D is located on \overline{BC} so that angle CAD is twice angle DAB. If AC/AD = 2/3, then CD/BD = m/n, where m and n are relatively prime positive integers. Find m+n.

\mathrm{(A) \ }10 \qquad \mathrm{(B) \ }14 \qquad \mathrm{(C) \ }18 \qquad \mathrm{(D) \ }22 \qquad \mathrm{(E) \ } 26

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