Details

The triangle formed by the intersection of the altitudes with the sides of a triangle ABC is called the orthic triangle of ABC.

The centroid of a triangle is the intersection of the lines drawn from the vertices to the midpoints of the opposite sides.

Let P be a point inside ABC. The reflections of the three lines AP, BP, and CP in the angle bisectors at A, B, and C meet in a point, called the isogonal conjugate of P.

The symmedian point is the isogonal conjugate of a triangle's centroid.