QA-P17: Involutary Conjugate of QA-P5


QA-P17 is the Involutary Conjugate of QA-P5.
 QA-P17-InvConj-ofQA-P5-01

As a consequence the line QA-P5.QA-P17 is the common tangent of the circumscribed conics P1.P2.P3.P4.QA-P5 and P1.P2.P3.P4.QA-P17.
 

QA-P17-00
QA-P17 is the intersection point of the tangents at the vertices of the QA-Diagonal Triangle and QA-P5 to the QA-DT-P5 Cubic (QA-Cu2).
 
 
Coordinates:  
1st CT-coordinate:
q r (2 p + q + r) (q r (q + r)2 - p (p + q + r) (q2 + r2))
1st DT-coordinate:
               p2 / ((p4 - (q2 - r2)2) - 2 p2 (-p2 + q2 + r2))
 
Properties:
  • QA-P17 lies on this QA-line:
        QA-P5.QA-P19
  • QA-P17 is the Involutary Conjugate (see QA-Tf2) of QA-P5.
  • QA-P17 lies on the Conic QA-Co5.
  • QA-P17 lies on the Cubics QA-Cu2 and QA-Cu4.
  • QA-P17 is the intersection point of the tangents at the vertices of the QA-Diagonal Triangle and QA-P5 to the QA-DT-P5 Cubic (QA-Cu2).
  • QA-P17 is the Isotomic Center of the Quadrangle formed by the vertices of the QA-Diagonal Triangle and QA-P5 (Isotomic Center).
 

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