BdMO(Regional) 2012 Problem

Geometry Level 3

In a circle, AB=4AB=4 is the diameter and OO is the centre. CC and DD are chosen such that C,O,DC,O,D are co-linear, COB=AOD=30\angle COB= \angle AOD=30^\circ, OC=ODOC=OD and BCO=90\angle BCO = 90^\circ. The perpendicular on ABAB through OO meets ACAC at EE and BDBD at FF.

If EF=abcEF=\frac{a\sqrt{b}}{c} where a,b,ca,b,c are integers and b,cb,c are primes, find the value of a+b+ca+b+c.

Note: CC and DD are not necessarily on the circumference of the circle.

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