QA-P7: QA-Nine-point Homothetic Center
The QA-Nine-point Homothetic Center (QA-P7) is the homothetic center of the Reference Quadrangle with the Quadrangle composed of four 2nd generation Nine-point Centers (point X(5) in ETC: Ref-12).
a4 q r/p + 3 p S2 + q SB2 + r SC2 + (p + q + r) (3 S2 + 2 SB SC)
-(3 S2 - SA2) p4 + (3 S2 + SA SB + SB c2) p2 q2 + (3 S2 + SA SC + SC b2) p2 r2 - a4 q2 r2
QA-P7 lies on this line:
- QA-P7.QA-P8 // QA-P2.QA-P4.QA-P6.
- QA-P7 is concyclic with QA-P2, QA-P8 and QA-P23.
- QA-P8 is the QA-Orthopole (QA-Tf3) of QA-P7. The QA-Orthopole of QA-P7 is a point on the line QA-P8.QA-P23 (ratio 2:1).