2004 AMC 10B Problem 24

In \bigtriangleup ABC we have AB = 7, AC = 8, and BC = 9. Point D is on the circumscribed circle of the triangle so that AD bisects \angle BAC. What is the value of \frac{AD}{CD}?

\mathrm{(A) \ } \frac{9}{8} \qquad \mathrm{(B) \ } \frac{5}{3} \qquad \mathrm{(C) \ } 2 \qquad \mathrm{(D) \ } \frac{17}{7} \qquad \mathrm{(E) \ } \frac{5}{2}

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