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


QG-Ci4 is the Circumcircle of the 2nd 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.

Infovisual QG-Ci4-infovisual-cvt-01.png
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.



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