Problem 1.

Let M,\,N two points interior to the circle \mathcal{C}(O) such that O is the midpoint of MN. Let S an arbitrary point lies on \mathcal C(O), and E,\,F the second intersections of the lines SM,\,SN with \mathcal C(O), respectively. The tangents in E,\,F with respect to the circle \mathcal C(O) intersect each other at I. Prove that the perpendicular bisector of the segment MN passes through the midpoint of SI.

(Mathematical Reflections 2007)

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