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Pairwise Tangent Circles Centered at the Vertices of a Triangle

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Let P, Q, and R be the points of tangency of the incircle with the sides of a triangle ABC. Draw circles with centers at A, B, and C that go through P, Q, and R as in the figure. Then those three circles are pairwise tangent.

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

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See Problem 13 in N. Altshiller-Court, College Geometry, 2nd ed., Mineola, NY: Dover, 2007 p. 93.

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