Mathot

Mathot point of a circular quadrangle

The orthogonals from the middles of the sides to the opposite sides of a circular quadrangle pass all through a fixed point M, symmetric of the center of the circumcircle with respect to the middle (gravity center) of the quadrangle.

From the center E of the circumcircle of a circular quadrangle ABCD draw the line (EN) joining E with the intersection point N of the lines joining opposite side-middles of the quadrangle. Extend EN to its double EM. EGMI is, by construction, a parallelogram, hence the line (IM) is orthogonal to CD, similarly to its parallel EG. Thus every orthogonal from the middle of one side to the opposite side passes through the remarkable point M, symmetric of the center of the circle with respect to the middle N of the quadrangle. M is called [the Mathot point (or anticenter) of the circular quadrangle].
Look at Mathot2.html for a further discussion.

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