Some general properties of four-points are discussed in FourPoints.html . Here is an illustration of the case in which the four points are on a circle (c), triangle EFG is obtuse and autopolar with respect to (c).

The three perspectivities, connected with the sides of triangle EFG are denoted here as {S

The triangle XYZ is generated from X by applying the involutions as shown. In particular, for X on the circle the whole triangle is inscribed in the circle. The center of the circle is the orthocenter of EFG and

FourPoints.html

Harmonic_Perspectivity.html

InversionAsInvolution.html

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