QA-P8: Midray Homothetic Center
The Midray Homothetic Center (QA-P8) is the homothetic center of the Reference Quadrangle with the 2nd generation Quadrangle composed of four Midray Circumcenters.
The Midray Circumcenters are the Circumcenters of the triangles Mij.Mik.Mil for all combinations of (i,j,k,l) ∈(1,2,3,4), where Mij = Midpoint(Pi,Pj), etc.
Coordinates:
1st CT-Coordinate:
-a4 q2 r2 + 2 b2 SC p2r2 + 2 c2 SB p2q2
+ 4 a2 SA p q r (p+q+r) + p q r (4 S2 p + a2 c2 q + a2 b2 r)
1st DT-Coordinate:
(3 S2 - SA2) p4 - (3 S2 + (SA - 3 c2) SB) p2 q2 - (3 S2 + (SA - 3 b2) SC) p2 r2 - 3 a4 q2 r2
Properties:
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QA-P8 lies on this line:
- QA-P8 is collinear with QA-P1 (Centroid) and the Reflection of QA-P4 in QA-P2.
- QA-P7.QA-P8 // QA-P2.QA-P4.QA-P6.
- QA-P8 is concyclic with QA-P2, QA-P7 and QA-P23.
- QA-P8 is the QA-Orthopole (QA-Tf3) of QA-P7.