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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