QA-P11: Circumcenter of the Diagonal Triangle
Coordinates:
1st CT-Coordinate:
- a2 q r (2 SA p2 q r + TA) + (SC TB p r + SB TC p q) + 2 S2 p2 q r (q+r) (p+q+r),
where:
TA = -a2 q2 r2 + b2 p2 r2 + c2 p2 q2
TB = +a2 q2 r2 - b2 p2 r2 + c2 p2 q2
TC = +a2 q2 r2 + b2 p2 r2 - c2 p2 q2
1st DT-Coordinate:
a2 SA
Properties:
- QA-P11 lies on these QA-lines:
- QA-P11 point is the center of the circumscribed circle through the vertices of the QA-Diagonal Triangle. This circle is interesting because QA-P2 (Euler-Poncelet Point) is situated on it.
- QA-P11 is the intersection point of the directrices of the 2 parabolas of the Reference Quadrangle.
- QA-P11 is collinear with QA-P10 (Centroid DT), QA-P12 (Orthocenter DT), QA-P13 (Nine-point Center DT) on the Euler Line of the QA-Diagonal Triangle.
- QA-P11 is the Gergonne-Steiner point (QA-P3) as well as the Isogonal Center (QA-P4) from the Quadrangle formed by the vertices of the Diagonal Triangle and QA-P2 (Euler-Poncelet Point).
- QA-P11 is concyclic with the Involutary Conjugate (see QA-Tf2) of QA-P11 and the foci of the QA-Parabolas QA-2Co1.
- QA-P11 is the QA-Orthopole(QA-Tf3) of QA-P12.
- QA-P11 is the Orthology Center of the QG-P1 Triple Triangle wrt the QG-P17 Triple triangle. See QA-Tr-1.
- QA-P11 is the Orthology Center of the QG-P2 Triple Triangle wrt the Triple triangles of QG-P1/QG-P4/QG-P8/QG-P15/QL-P12. See QA-Tr-1.
- QA-P11 is the Orthology Center of the QG-P8 Triple Triangle wrt the Triple triangles of QG-P5,QG-P10,QL-P2. See QA-Tr-1.
- The reflection of QA-P11 in QA-P1 is the midpoint of QA-P5 and QA-P12.