As a consequence the line QA-P18.QA-P19 is the common tangent of the circumscribed conics P1.P2.P3.P4.QA-P18 and P1.P2.P3.P4.QA-P19.
QA-P18 is the intersection point of the tangents at the vertices of the QA-Diagonal Triangle and QA-P19 to the QA-DT-P19 Cubic (QA-Cu4).
Coordinates:
1st CT-coordinate:
p (q2 + r2) (2 p + q + r) (p2 + p q + p r - q r)
1st DT-coordinate:
p2 / (-p2 + q2 + r2)
Properties:
- QA-P18 lies on this QA-line:
- QA-P18 is the Involutary Conjugate (see QA-Tf2) of QA-P19.
- QA-P18 lies on the QA-DT-P19 Cubic (QA-Cu4).
- QA-P18 also lies on the tangent at QA-P19 to the QA-DT-P19 Cubic (QA-Cu4), which is also the tangent at QA-P19 to the Conic (P1,P2,P3,P4,QA-P19), which is also the tangent at QA-P18 to the Conic (P1,P2,P3,P4,QA-P18).