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R,S and T collinear, very nice!

Source: Oliforum math contest, problem 3

September 30, 2009
geometryincentercircumcirclesearchcyclic quadrilateralangle bisector

Problem Statement

Let a cyclic quadrilateral ABCD ABCD, AC \cap BD \equal{} E and let a circle Γ \Gamma internally tangent to the arch BC BC (that not contain D D) in T T and tangent to BE BE and CE CE. Call R R the point where the angle bisector of ∠ABC \angle ABC meet the angle bisector of ∠BCD \angle BCD and S S the incenter of BCE BCE. Prove that R R, S S and T T are collinear. (Gabriel Giorgieri)
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