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Maltitudes, Circumcircles and Circumcenters

For any quadrilateral one can define the so-called maltitudes. A maltitude on a side of a quadrilateral is defined as the line through the midpoint of the
side and perpendicular to the opposite side. Generally the four maltitudes of a quadrilateral are not concurrent, but if the quadrilateral is cyclic they are.

Prove that indeed the maltitudes of any cyclic quadrilateral ABCD are concurrent and that their point of concurrency is the reflection of the
circumcenter of ABCD in the center point of ABCD.

The circumcircle to ABCD is obtained by drawing lines through the midpoints of the sides and perpendicular
to the sides themselves. Look for parallelograms and keep in mind that the diagonals of a parallelogram bisect each other.

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