# Michael starts with ABC

Geometry Level pending

$$\Gamma$$ is a circle with a diameter $$BC$$, $$A$$ is a point on $$BC$$ such that $$AB = 3$$ and $$AC = 9,$$ and $$D$$ is a point on circle $$\Gamma$$ such that $$\overline{AD} \perp \overline{BC}.$$ The tangents to circle $$\Gamma$$ at points $$B$$ and $$D$$ intersect at $$E.$$ The line from $$E$$ that is parallel to line $$BC$$ intersects the circle at points $$F$$ and $$G,$$ such that $$F$$ is between $$E$$ and $$G.$$ The area of $$\triangle CGE$$ can be expressed in the form $$\sqrt{a} + \sqrt{b},$$ where $$a$$ and $$b$$ are positive integers. What is the value of $$a+b?$$

This problem is posed by Michael T.

×