Loci Of Midpoints Of Pedal Triangles
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Abstract: Given a reference triangle, we investigate the loci of the midpoints of the pedal triangle as the pedal point runs round a circle. These loci are ellipses whose principal axes align with the angle bisectors of the reference triangle. We show that the axes of these ellipses intersect in a common point if and only if the center of the circle lies on the line joining the incenter to the circumcenter, in which case the intersection of the axes lies on the Nagel Line. Issue: Volume 1 Pages: 1 - 6 |
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