Let A X be a diameter of a circle \Omega with radius 10, and suppose that C lies on \Omega so that A C=16. Let D be the other point on \Omega so C X=C D. From here, define D^{\prime} to be the reflection of D across the midpoint of A C, and X^{\prime} to be the reflection of X across the midpoint of C D. If the area of triangle C D^{\prime} X^{\prime} can be written as \frac{p}{q}, where p, q are relatively prime, find p+q.