QA-P17: Involutary Conjugate of QA-P5

QA-P17 is the Involutary Conjugate of QA-P5.

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 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).

1^st CT-coordinate

q r (2 p + q + r) (q r (q + r)² – p (p + q + r) (q² + r²))

1^st 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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