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.

5P s P1 Center Circumscribed Conic 01

Properties:
5P-s-P1 is also the common point of the radical axes of the 5 versions of QA-Ci1 (Circumcircle of the Diagonal Triangle) in the 5-Point.
5P-s-P1 is also the common point of the 5 versions of QA-Co1 (Nine Point Conic) in the 5-Point.
5P s P1 QA Co1 NPC Common Point 01
5P-s-Tf3(5P-s-P1) = 5P-s-P1.