Pedal Point at Circumcenter of Triangle ABC

When the pedal point is located at the circumcenter of triangle ABC, The pedal triangle and the medial triangle are the same triangle. This can be seen from the following picture because the side of triangle ABC that is parallel to its corresponding side of the pedal triangle has a ratio of 2 to 1. Thus the vertices of the pedal triangle are located at the midpoints of the sides of triangle ABC.

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