QL-P9: Circumcenter QL-Diagonal Triangle
4 m n (-4 Δ2 m2 n2 + a2 l3 (SC m + SB n) - l2 (SC m + SB n)2 + l m n (SB b2 m + SC c2 n))
SA = (–a2 + b2 + c2)/ 2 SB = (+a2 – b2 + c2)/ 2 SC = (+a2 + b2 – c2)/ 2
Δ = Area = 1/4 √[(a + b + c) (-a + b + c) (a - b + c) (a + b - c)]
- QL-P9 lies on these lines:
- QL-P9 lies together with QL-P8, QL-P10 and QL-P11 on QL-L7, the QL-Euler Line of the Diagonal Triangle. The ratio of distances between QL-P9, QL-P8, QL-P11, QL-P10 in this order is 2 : 1 : 3.
- QL-P9.QL-P16 // QL-P1.QL-P11.
- QL-P1 lies on the Polar (see Ref-13, Polar) of QL-P9 wrt QL-Co1.
- QL-P9 lies on the circumcircle of the triangle formed by the 3 QL-versions of QG-P9.
- The Clawson-Schmidt Conjugate (QL-Tf1) of QL-P9 lies on QL-Ci3 (Miquel Circle).
- The directrices of QL-Co1 and QL-Co3 meet in QL-P9 (Circumcenter QL-Diagonal Triangle).