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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