John Wentworth Clawson calls this point the Focal Point. This point is also known as the Wallace Point and the Miquel Point. For each of the four triangles in the quadrilateral, construct the circumcircle. In the sketch below, the conclusion is rather evident. Slowly drag the PURPLE slider to the left to reveal each circumcircle, one at a time, until all are shown.
Play around with this a little bit. What happens when two sides of the quadrilateral are parallel? What happens when two pairs of sides are parallel?
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