QA-P28: Midpoint of the foci of the QA-Parabolas

QA-P28 is the Midpoint of the foci F1 and F2 of the pair of circumscribed QA-Parabolas (QA-2Co1) .
Because these parabolas only can be constructed when the Reference Quadrangle is not concave a better definition of this point is: “the point on the line QA-P4.QA-P10 such that its distance relation to these points is resp. 3 : 1”.
But because the property related to the parabolas is much more appealing this point has been called after its primary function.
It also can be reasoned that in a concave quadrangle this point represents the Midpoint of the foci of the imaginary parabolas. Coordinates:

1st CT-Coordinate:
(q + r) (-a4 q r (p + q) (p + r) (3 p2 + 2 p q + 2 p r + q r)
-  p2 (q + r) (2 p + q + r) (c4 p q + b4 p r + (b2 - c2)2 q r)
+ p q r (5 p2 + 3 p q + 3 p r + q r) (a2 b2 (p + q) + a2 c2 (p + r)))
1st DT-Coordinate:
-2 b2 c2 p4 - a2 c2 q4 - a2 b2 r4 + c2 (3 SC - SB) p2 q2 + b2 (3 SB - SC) p2 r2 + a2 ( c2 + b2) q2 r2

Properties:
• QA-P28 lies on these QA-lines:
QA-P4.QA-P10          (3 : 1)
QA-P6.QA-P29          (1 : 1 => QA-P28 = Midpoint QA-P6.QA-P29)

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