QL-P17: QL-Adjunct Quasi Circumcenter
QL-P17 is the 2nd common intersection point of the coaxal circumcircles of the 3 triangles formed by the 3 QL-versions of resp. QG-P1, QG-P5, QG-P9.
The 1st intersection point of these circles is QL-P16 (QL-Quasi Circumcenter).
Coordinates:
1st CT-coordinate:
m n (a2 ( l - m) ( l - n) (2 l2 (m - n)2 - m2 n2 + l m n (m + n))
+ b2 (m - n) (m - l) n l (-3 l m + l n + m n)
+ c2 (n - m) (n - l) m l (l m - 3 l n + m n)))
1st DT-coordinate:
a2 m2 n2 / (m2-n2)
Properties:
- QL-P17 lies on these lines:
- QL-P17 is the AntiComplement of QL-P25 wrt the QL-Diagonal Triangle.
- QL-P25 lies on the polar of QL-P17 wrt the Polar Circle of the QL-Diagonal Triangle (note Eckart Schmidt).
- QL-P17 lies on the Dimidium Circle QL-Ci6. The second intersection point with the circumcircle of the QL-Diagonal Triangle (QL-Ci1) is QL-P24.