The isogonal conjugate of the circumcircle is the line at infinity, given in trilinear coordinates by 0 } } and in barycentric coordinates by 0 } }.
12.
By the isogonal conjugate article, in trilinear coordinates the conjugate of x : y : z is 1 / x : 1 / y : 1 / z.
13.
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?
14.
:: : : : : : If the point is on an angle bisector, its isogonal conjugate is on the other side of the incenter, never on the same side.
15.
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.
16.
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.
17.
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.
18.
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.
19.
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.
20.
Can two isogonal conjugates ever be collinear with the incenter in a non-isosceles triangle ? ( The trivial / degenerate triplet incenter incenter incenter is also excluded ) . talk ) 06 : 51, 1 July 2016 ( UTC)
