Since the circumcenter does not always stay inside the circle, it is surprising that the pedal triangle, whose pedal point is the circumcenter, stays within the original triangle, even when it is obtuse.
Since the Circumcenter is defined as the point of concurrency of the perpendicular bisectors, the feet of the pedal triangle must be the midpoints of the sides of the triangle. This means, that by definition, this pedal triangle is in fact the medial triangle.
Since the vertices of the medial triangle are on the Nine Point Circle, the circumcircle of this Pedal Triangle is the Nine Point Circle.
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