QA-P40 Centroid of the QL-P6-Triple Triangle

QA-P40 is the Centroid of the QL-P6-Triple Triangle.
It is also the Centroid of the QG-P9-Triple Triangle.
It is also the Circumcenter of the QL-P17-Triple Triangle.
For the definition of a Px-Triple Triangle see QA-1. 1st CT-Coordinate:
-a4 (p + q) (p + r) (4 q2 + 6 q r + 4 r2 + 5 p (q + r)) + (-b2 + c2) p (q + r) (-c2 (p + r) (2 p + 3 q + r)
+ b2 (p + q) (2 p + q + 3 r)) + a2 (c2 (p + r) (q (3 p + 2 q)2 + (7 p2 + 15 p q + 6 q2) r + (5 p + 2 q) r2)
+ b2 (p + q) (2 r (q + r) (q + 2 r) + p2 (7 q + 9 r) + p (5 q2 + 15 q r + 12 r2)))

1st DT-Coordinate:
a4 (3 p4 + q4 + 6 q2 r2 + r4 - 4 p2 (q2 + r2)) + 2 (b - c) (b + c) p2 (b2 (p2 - q2 - 3 r2) + c2 (-p2 + 3 q2 + r2))
- a2 (b2 (5 p4 + (q2 - r2)2 - 2 p2 (3 q2 + r2)) + c2 (5 p4 + (q2 - r2)2 - 2 p2 (q2 + 3 r2)))

Properties:
QA-P11.QA-P32          (2 : 1)
QA-P14.QA-P26          (3 : -1)
QG-P9.QL-P6              (2 : 1)
Midpoint(QA-P5,QA-P12) . Midpoint(QA-P1,QA-P32)       (4 : -1)
the Circumcenter of the QL-P17-Triple Triangle
the Centroid of the QL-P6-Triple Triangle
the Centroid of the QG-P9-Triple Triangle

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