We get more nice figures, if we look for a first generalization of the WALLACE-lines. Let X be a point on the circumcircle u of a triangle ABC. Instead of perpendicular lines we consider the isoclinal lines through the point X rotated by the angle a and get a straight line [P*Q*R*] as well.
Figure 5 shows the envelope of the lines [P*Q*R*] changing a and leaving X fixed. We get a parabola with the focus X and the WALLACE-line [PQR] of X as the tangent at the vertex of the parabola. Figure 6 shows the envelope of the lines [P*Q*R*] leaving a fixed and moving X. We get a hypocycloid of STEINER again. |