5P-s-Co1 5P-Circumscribed Conic

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.

See Ref-19.
1. Given five points A, B, C, D, E.
2. Let l be a variable line through E. (Draw a circle center E with any radius. Let L be an arbitrary point on the circle, and take l to be the line EL.)
3. The line joining AB.DE and BC.l cuts CD in Z, then P = AZ.l lies on the conic.
As L moves round the circle, P traces the conic. (Select L and P, and Construct/Locus.)

Tangents at 5P-s-Co1
The construction of tangents at 5P-s-Co1 can be found at QA-Tf9 (5th point tangent).

5P s Co1 Circumscribed Conic 01

• Given Pentangle P1P2P3P4P5. The vertices of the AntiCevian Triangle of P1 wrt the Diagonal Triangle (QA-Tr1) of Quadrangle P2P3P4P5 lie on the conic 5P-s-Co1. Points P1, P2, P3, P4, P5 can be interchanged for this property. See [34], QFG#3517.