QG-Ci4: Circumcircle of the 2^nd QG-Quasi Diagonal Triangle

QG-Ci4 is the Circumcircle of the 2^nd QG-Quasi Diagonal Triangle QG-Tr2.

This circumcircle is special because many points lie on this circle.

It was found by Eckart Schmidt, December 27, 2012. See also [34] QFG, messages #347 and #530.

Equation:

If we use QL-Tr1 as reference triangle, this circle has the equation:

a²(l²-m²)(n² x+m² y+n² z) z – c²(m²-n²)(l² x+m² y+l² z) x + b²(l²-m²)(m²-n²) z x = 0

Properties

• QG-Ci4 contains these points:
  • the Diagonal Crosspoint QG-P1,
  • the diagonal midpoints M1 and M2,
  • the 1st QG-Quasi Circumcenter QG-P5,
  • the Gergonne-Steiner Point QA-P3,
  • the QL-Adjunct Quasi Circumcenter QL-P17
  • two vertices of the Miquel Triangle (QA-Tr2) unequal QL-P1.
• The center of QG-Ci4 is QG-P9.

Estimated human page views: 788