QL-P8: Centroid QL-Diagonal Triangle

QL-P8 is the Centroid of the Diagonal Triangle (QL-Tr1) of the Reference Quadrilateral.

1^st CT-coordinate

(l m + l n – m n)² m n – 4 (l – m) (l – n) m² n²    (note that this formula is independent of a,b,c)

1^st DT-coordinate

1

Properties

• QL-P8 lies on these lines:
  • QL-P1.QL-P24
  • QL-P9.QL-P10 =QL-L7        ( 1 : 2)
  • QL-P12.QL-P14=QL-L8       (-3 : 4)
  • QL-P17.QL-P25                    ( 2 : 1)
• The ratio of distances between QL-P9, QL-P8, QL-P11, QL-P10 in this order is 2 : 1 : 3.
• The ratio of distances between QL-P8, QL-P15, QL-P12, QL-P14, QL-P18 in this order is 2 : 1 : 1 : 2.
• d(QL-P8, QL-L9) = 2 * d(QL-P12, QL-L9) =4/3 * d(QL-P19, QL-L9)
• QL-P8 is also Centroid of the Triangle formed by the 3 QL-versions of QA-P20 (note Eckart Schmidt).
• QL-P8 lies on the Polar (see [13], Polar) of QL-P12 wrt QL-Co1 and vice versa.

Estimated human page views: 498