Let the inner and outer Soddy triangles of a reference triangle Δ A B C be denoted Δ P Q R and Δ P' Q' R', respectively. Similarly, let the tangential triangles of Δ P Q R and Δ P' Q' R' be denoted Δ X Y Z and Δ X' Y' Z', respectively. Then the inner (respectively, outer) Rigby point Ri (respectively, Ri') is the perspector of Δ P Q R and Δ X Y Z (respectively, Δ P' Q' R' and Δ X' Y' Z'). The Rigby points lie on the Soddy line. They have triangle center functions α_Ri | = | 1 + (8Δ)/(3a(b + c - a)) α_Ri' | = | 1 - (8Δ)/(3a(b + c - a)),

contact triangle | first Eppstein point | Gergonne point | Griffiths points | incenter | orthopole | second Eppstein point | Simson line | Soddy centers | Soddy triangles | tangential triangle