MathDB
2008 KMO P6

Source:

August 9, 2015
geometryconcurrence

Problem Statement

Let ABCDABCD be inscribed in a circle ω\omega. Let the line parallel to the tangent to ω\omega at AA and passing DD meet ω\omega at EE. FF is a point on ω\omega such that lies on the different side of EE wrt CDCD. If AE⋅AD⋅CF=BE⋅BC⋅DFAE \cdot AD \cdot CF = BE \cdot BC \cdot DF and ∠CFD=2∠AFB\angle CFD = 2\angle AFB, Show that the tangent to ω\omega at A,BA, B and line EFEF concur at one point. (AA and EE lies on the same side of CDCD)
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