QL-Ci1: QL-Circumcircle Diagonal Triangle

 
QL-Ci1 is the circumcircle of the QL-Diagonal Triangle (see QL-TR1 and QG-P1).
QL-P9 is its center.
 
 
QL-Ci1-QL-Circumcircle-DT
 
Equations/Radii 
Equation of Circle in CT-notation:
     l2 ( l m + l n - m n) (b2 m2 + c2 n2 - 2 SA m n) x2
+ m2 ( l m - l n + m n) (c2 n2 + a2 l2  - 2 SB l n) y2
+ n2 (-l m + l n + m n) (a2 l2 + b2 m2 - 2 SC l m) z2
+ 2 (SC l2 m2 + SB l2 n2 + SA m2 n2) (l m x y + l n x z + m n y z) = 0
Radius2 of Circle in CT-notation:
   (a2 l2  - a2 l m - b2 l m + c2 l m + b2 m2)
* (a2 l2  - a2 l n + b2 l n - c2 l n + c2 n2)
* (b2 m2 + a2 m n - b2 m n - c2 m n + c2 n2)
* l2 m2 n2 / (4 Δ 2 (l m - l n - m n)2 (l m + l n - m n)2 (l m - l n + m n)2)
where: Δ = Area = 1/4 √[(a + b + c) (-a + b + c) (a - b + c) (a + b - c)]
 
Equation of Circle in DT-notation:
            a2 y z + b2 x z +c2 x y = 0
Radius2 of Circle in DT-notation:  
            a2 b2 c2 / (4 S2)
 
 
Properties:
  • QL-P16 (QL-Quasi Circumcenter) and QL-P17 (QL-Adjunct Quasi Circumcenter) and QL-P24 (Intersection QL-P1.QL-P8 ^ QL-P13.QL-P17) lie on QL-Ci1.
  • QL-Ci1 is orthogonal wrt the Plücker Circle (QL-Ci5).
  • QL-Ci1 is the locus of Euler-Poncelet points (QA-P2) of the Quadrangle formed by the tangential points of the QL-tangential conics. See Ref-34, QFG #357 by Eckart Schmidt.

 

Add a comment


Antispam code
Renew