Given a triangle Δ A B C, construct the contact triangle Δ D E F. Then the Nobbs points are the intersections of the corresponding sides of triangles Δ A B C and Δ D E F, i.e., the first Nobbs point D' is the intersection of E F and B C, and similarly for E' and F'. The Nobbs points are collinear and fall along the Gergonne line. They have trilinear coordinates -(a - b + c) b:(-a + b + c) a:0, 0: - (a + b - c) c:(a - b + c) c, and (a + b - c) c:0: - a(-a + b + c). Given the tangent circles of a reference triangle, the pairwise external centers of similitude are the Nobbs points.

collinear | contact triangle | Evans point | Fletcher point | Gergonne line | perspective triangles