This system of circles determines a one parametric family of cyclic quadrilaterals whose diagonals pass through F. More precisely, for each point N of the arc (XY) of the circle (e), containing the point A, there is one and only one cyclic quadrilateral (q) inscribed in (c) with the properties:

1) The point N* is the other intersection point of (e) and the line NC. The diagonals of (q) intersect at F and have their middles at N, N* respectively.

2) The pairs of opposite sides of (q) intersect at the diametral points D, E of circle (d).

3) The centroids of (q), coincide with the middles of NN* and lie on the arc (XHY) of the circle with diameter CH.

I call (d) the [Orthocycle] of the cyclic quadrilateral. It seems to be connected with many properties of the cyclic quadrilateral (q).

All the properties follow directly from the discussion made in the file CyclicProjective.html .

Fixing the system of the two circles and the point (c,d, F) and varying only N, there is a particular place for N for which the corresponding quadrilateral q becomes [bicentric]. See the file Orthocycle2.html .

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