A Line Associated with an Excircle

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An excircle is a circle drawn outside a triangle that is tangent to the extensions of two of its sides and to the third side.


Let ABC be a triangle. Then these three points are collinear: (1) the point of tangency of the excircle opposite A, (2) the incenter of ABC, and (3) the midpoint of the altitude of ABC from A.


Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA



See problem 5 in Classical Theorems in Plane Geometry.

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