Given a triangle Δ A B C with inner and outer Soddy centers S and S', respectively, the inner Soddy triangle Δ P Q R (respectively, outer Soddy triangle Δ P' Q' R') is the triangle formed by the points of tangency of the inner (respectively, outer) Soddy circle with the three mutually tangent circles centered at each of the vertices of Δ A B C These triangles were explicitly mentioned but not named by Oldknow. The name "Soddy triangles" is therefore proposed here for the first time.
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