QA-P13: Nine-point Center of the QA-Diagonal Triangle
It is also the center of the circumcircle of the Medial Triangle (MT) of the QA-Diagonal Triangle (DT).
The sides of the MT are tangential to both Quadrangle Parabolas.
- a2 q r (2 SA p2 q r + TA) + (SC TB p r + SB TC p q) – 2 S2 p2 q r (q+r) (3p+q+r),
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
S2 + SB SC
- QA-P13 lies on these QA-lines:
- QA-P13 = Midpoint of QA-P11.QA-P12.
- QA-P13 = the center of QA-Ci2, the circumcircle of the Medial Triangle (MT) of the QA-Diagonal Triangle (DT).
- QA-P13 = QA-Centroid (QA-P1) of the quadrangle formed by the vertices of the Diagonal Triangle and QA-P12.
- QA-P13 = QA-Centroid of Quadrangle QA-P2.QA-P3.QA-P12.QA-P20.
- QA-P13 is the Orthology Center of the QG-P2 Triple Triangle wrt the QG-P17 Triple triangle. See QA-Tr-1.