# 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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