5P-s-P1: 5P-Circumscribed Conic Center
It is well known that in a system of 5 random Points a unique circumscribed conic can be constructed.
This conic is 5P-s-Co1 and its center is 5P-s-P1.
Construction (See Ref-19):
1. Let the conic be defined by points A, B, C, D, E.
2. Let the tangents at A, B meet at T, and those at B, C meet at TO.
3. Let M, MO be the midpoints of AB and BC, then the center O is MT.MOTO.
Construction of Conic Tangents:
4. Let d = AB, e = BC, a = CD, b = DE, c = EA, then bd.ce cuts a in a point lying on the tangent at A.