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Show that P, E an F are collinear

Source: Chinese Mathematical Olympiad 1997 Problem 4

August 26, 2013
geometrycircumcirclecyclic quadrilateral

Problem Statement

Consider a cyclic quadrilateral ABCDABCD. The extensions of its sides AB,DCAB,DC meet at the point PP and the extensions of its sides AD,BCAD,BC meet at the point QQ. Suppose   QE,QF are tangents to the circumcircle of quadrilateral ABCDABCD at E,FE,F respectively. Show that P,E,FP,E,F are collinear.
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