# Distance from the Center

Geometry Level 5

Circle $$\Gamma$$ with center $$O$$ has diameter $$AB = 192$$. $$C$$ is a point outside of $$\Gamma$$, such that $$D$$ is the foot of the perpendicular from $$C$$ to $$AB$$ and $$D$$ lies on the line segment $$OB$$. From $$C$$, a tangent to $$\Gamma$$ is drawn, touching $$\Gamma$$ at $$E$$, where the foot of the perpendicular from $$E$$ to $$AB$$ lies within $$AD$$. $$CD$$ intersects $$EB$$ at $$F$$. If $$CF = 110$$, what is the length of $$OC$$?

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