# Reciprocal Sum in a Circle

Geometry Level 4

Triangle $$ABC$$ has circumcenter $$O$$ and circumradius $$R = 0.025$$. Let $$AO$$ intersect $$BC$$ at $$D$$, $$BO$$ intersect $$CA$$ at $$E$$, and $$CO$$ intersect $$AB$$ at $$F$$. What is the value of

$\frac {1}{AD} + \frac {1}{BE} + \frac {1}{CF}?$

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