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2

Part of 2011 Benelux

Problems(1)

Perpendicular Bisector of Angle Bisector, Concyclic Points

Source: Benelux Mathematical Olympiad 2011, Problem 2

5/7/2011
Let ABCABC be a triangle with incentre II. The angle bisectors AIAI, BIBI and CICI meet [BC][BC], [CA][CA] and [AB][AB] at DD, EE and FF, respectively. The perpendicular bisector of [AD][AD] intersects the lines BIBI and CICI at MM and NN, respectively. Show that AA, II, MM and NN lie on a circle.
geometryincentercircumcircleperpendicular bisectorcyclic quadrilateralangle bisector