MathDB
Question 3

Source: Iran TST 2006

April 29, 2006
geometryparallelogramcircumcirclegeometric transformationreflectionconicsangle bisector

Problem Statement

Let l,ml,m be two parallel lines in the plane. Let PP be a fixed point between them. Let E,FE,F be variable points on l,ml,m such that the angle EPFEPF is fixed to a number like α\alpha where 0<α<π20<\alpha<\frac{\pi}2. (By angle EPFEPF we mean the directed angle) Show that there is another point (not PP) such that it sees the segment EFEF with a fixed angle too.
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