Distance from the Center

Geometry Level 5

Circle Γ \Gamma with center OO has diameter AB=192AB = 192 . CC is a point outside of Γ\Gamma, such that DD is the foot of the perpendicular from CC to ABAB and DD lies on the line segment OBOB. From CC, a tangent to Γ\Gamma is drawn, touching Γ\Gamma at EE, where the foot of the perpendicular from EE to ABAB lies within ADAD. CDCD intersects EBEB at FF. If CF=110CF = 110, what is the length of OCOC?

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