Friday, March 19, 2010

The Complete Quadrilateral: Circles on Diagonals

Construct the diagonals of the quadrilateral, and then construct circles with the diagonals as diameters. The centers of the circles are the midpoints of the diagonals, and we know they lie on the Midline. The three circles intersect in two distinct points on the Orthocentric Line. Therefore, the Midline and the Orthocentric Line are perpendicular. In circle-talk, these three circles are coaxal, and the Orthocentric Line is the radical axis of the three circles.

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