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IGO - Hard level - Problem 2

Source:

September 3, 2015
IGOgeometry

Problem Statement

let ABC ABC an equilateral triangle with circum circle w w
let P P a point on arc BC BC ( point A A is on the other side )
pass a tangent line d d through point P P such that P∩AB=F P \cap AB = F and AC∩d=L AC \cap d = L
let O O the center of the circle w w
prove that ∠LOF>900 \angle LOF > 90^{0}
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