QL-P24: Intersection QL-P1.QL-P8 ^ QL-P13.QL-P17


QL-P24 is the point of intersection of the lines QL-P1.QL-P8 and QL-P13.QL-P17.
It is also one of the points of intersection of the circles QL-Ci1 (Circumcircle QL-Diagonal Triangle) and QL-Ci6 (Dimidium Circle).
                       
QL-P24-Intersectionpoint P1-P8 and P16-P23
 
Coordinates:  
1st CT-coordinate:
(l - m) (l - n) m n
* (Tmn (a4 (4 (l - m) (l - n) (l m - l n - m n) (l m - l n + m n) + (l m + l n - m n))
               + b4 (m - n) (+l m - l n + m n) / (l - n)
               + c4 (m - n) (-l m + l n + m n) / (m - l) - 2 b2 c2 (m - n)2)
                - 2 a2 b2 ((l - m) (m - n) Tnl - (l m - l n + m n) Tlm)
    - 2 a2 c2 ((l - n) (m - n) Tlm - (l m - l n - m n) Tnl))
where:
Tmn = (l2 m2 - 2 l2 m n + 2 l m2 n + l2 n2 + 2 l m n2 - 3 m2 n2)
Tlm = (l2 m2 + 2 l2 m n - 2 l m2 n - 3 l2 n2 + 2 l m n2 + m2 n2)
Tnl   = (3 l2 m2 - 2 l2 m n - 2 l m2 n - l2 n2 + 2 l m n2 - m2 n2)
1st DT-coordinate:
            (a2 (l2-n2)+b2 (m2-n2)) (a2 (l2-m2)+c2 (-m2+n2))

Properties:
        QL-P1.QL-P8
        QL-P13.QL-P17
  • QL-P24 is the projection of QL-P16 on the line QL-P1.QL-P8.
  • QL-P24 is one of the points of intersection of the circles QL-Ci1 (Circumcircle QL-Diagonal Triangle) and QL-Ci6 (Dimidium Circle). The other point of intersection is QL-P17 (QL-Adjunct Quasi Circumcenter).
 


 
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