For a point P with trilinear coordinates p : q : r, the isogonal conjugate P'is at 1 / p : 1 / q : 1 / r, and the incenter I is at 1 : 1 : 1.
22.
Any triangle with angles A, B, C combined with a point p : q : r satisfying this gives a right angle from P to the incenter to the isogonal conjugate of P . But do any solutions of this, satisfying the constraint on the cosines of a triangle ( and satisfying p, q, r ` " 0 as required for isogonal conjugates to be defined ), exist?
23.
Any triangle with angles A, B, C combined with a point p : q : r satisfying this gives a right angle from P to the incenter to the isogonal conjugate of P . But do any solutions of this, satisfying the constraint on the cosines of a triangle ( and satisfying p, q, r ` " 0 as required for isogonal conjugates to be defined ), exist?
