complete quadrilateral (1234).

The Miquel point of (1234) is the common point

of the circles (123), (234), (341), (412)

[and also the circle (O(123)O(234)O(341)O(412))

ie the circle passing through the four O's of the

triangles (123), (234), (341), (412)]

Now, define the Miquel point of (1234)

by using only LINES; not circles.

Antreas