Pairwise Tangent Circles Centered at the Vertices of a Triangle

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.

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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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Related Curriculum Standards

US Common Core State Standards, Mathematics