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 Ref-34, QFG, messages #347 and #530.
 
QG-Ci4-Circumcircle-QG-Tr2-01
 
 
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.

 

 

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