What is the minimum angle formed by the incenter with two isogonal conjugates ? ( For instance, in the case of centroid-incenter-symmedian point, it is 160?
42.
:: : : : : : If the point is on an angle bisector, its isogonal conjugate is on the other side of the incenter, never on the same side.
43.
For each point " P " on the cubic but not on a sideline of the cubic, the isogonal conjugate of " P " is also on the cubic.
44.
The Darboux cubic may be defined from the de Longchamps point, as the locus of points X such that X, the isogonal conjugate of X, and the de Longchamps point are collinear.
45.
Some of the isogonal tetracontagrams are depicted below, as a truncation sequence with endpoints t { 20 } = { 40 } and t { 20 / 19 } = { 40 / 19 }.
46.
Specifically, let T be a triangle, and A, B, and C its inverse with respect to the circumcenter of T of the isogonal conjugate or the nine-point center of T.
47.
Goormaghtigh proved that N'is the inverse with respect to the circumcircle of T of the isogonal conjugate of the point Q on the Euler line OH, such that QH / QO = 2t.
48.
For example, the isogonal conjugate of a line is a circumconic; specifically, an ellipse, parabola, or hyperbola according as the line intersects the circumcircle in 0, 1, or 2 points.
49.
Many isogonal tetracontagrams can also be constructed as deeper truncations of the regular icosagon { 20 } and icosagrams { 20 / 3 }, { 20 / 7 }, and { 20 / 9 }.
50.
Many isogonal triacontadigrams can also be constructed as deeper truncations of the regular hexadecagon { 16 } and hexadecagrams { 16 / 3 }, { 16 / 5 }, and { 16 / 7 }.
