IMO Shortlist 1994 problem G5

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Dodao/la: arhiva
2. travnja 2012.
A circle C with center O. and a line L which does not touch circle C. OQ is perpendicular to L, Q is on L. P is on L, draw two tangents L_1, L_2 to circle C. QA, QB are perpendicular to L_1, L_2 respectively. (A on L_1, B on L_2). Prove that, line AB intersect QO at a fixed point.

Original formulation:

A line l does not meet a circle \omega with center O. E is the point on l such that OE is perpendicular to l. M is any point on l other than E. The tangents from M to \omega touch it at A and B. C is the point on MA such that EC is perpendicular to MA. D is the point on MB such that ED is perpendicular to MB. The line CD cuts OE at F. Prove that the location of F is independent of that of M.
Izvor: Međunarodna matematička olimpijada, shortlist 1994