Geometry Ratio

Geometry Level pending

In \(ABC\), let \(I\) be the center of the inscribed circle and let the bisector of angle \(ACB\) intersect line \(AB\) at \(C\). The line through \(C\) and \(I\) intersect the circumscribed circle of triangle \(ABC\) at the two points \(C\) and \(D\). If angle I=2 and angle D=3, then \(IC=\frac{p}{q}\), where \(p \) and \(q\) are coprime positive integers. Find \(p + q \).

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