- Steve Phelps
A generalization of the nine-point circle. Draw the cevians through point P. The conic passes through the points where the cevians intersect the opposite sides, the midpoints of the sides, and the midpoints of the segments drawn from P to the vertices of the triangle. The ratio PN:NG = 3:1, regardless of the location of P Drag point P to point H (orthocenter) and the conic is the nine-point circle. Drag point P to point G (centroid( and the conic is the Steiner Inellipse.