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