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Concyclic Points Associated with an Angle Bisector and an Excircle


	Let ABC be a triangle with incenter I and circumcenter O, and let J be the excenter opposite A. Let the angle bisector from A intersect the circumcircle at M. Then B, C, I, and J lie on a circle centered at M.


	Contributed by: Jay Warendorff

See problem 2.4(a) in V. Prasolov, Problems in Plane and Solid Geometry, Vol. 1, Plane Geometry [PDF], (D. Leites, ed. and trans.).

Angle Bisector (Wolfram MathWorld)

Circumcenter (Wolfram MathWorld)

Circumcircle (Wolfram MathWorld)

Concyclic (Wolfram MathWorld)

Excenter (Wolfram MathWorld)

Incenter (Wolfram MathWorld)

"Concyclic Points Associated with an Angle Bisector and an Excircle" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/ConcyclicPointsAssociatedWithAnAngleBisectorAndAnExcircle/

Contributed by: Jay Warendorff

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