Reciprocal Sum in a Circle

Geometry Level 4

Triangle ABCABC has circumcenter OO and circumradius R=0.025 R = 0.025 . Let AOAO intersect BCBC at DD, BOBO intersect CACA at EE, and COCO intersect AB AB at FF. What is the value of

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

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