Triangle A B C is inscribed in a unit circle \omega. Let H be its orthocenter and D be the foot of the perpendicular from A to B C. Let \triangle X Y Z be the triangle formed by drawing the tangents to \omega at A, B, C. If A H=H D and the side lengths of \triangle X Y Z form an arithmetic sequence, the area of \triangle A B C can be expressed in the form \frac{p}{q} for relatively prime positive integers p, q. What is p+q?