QA-P19: AntiCompl. QA-P16 wrt QA-DT

QA-P19: AntiComplement of QA-P16 wrt the QA-Diagonal Triangle

QA-P19 is the AntiComplement of QA-P16 wrt the QA-Diagonal Triangle.

QA-P19 has several properties. See properties below.

QA-P19 is the intersection point of the tangents at the vertices of the Reference Quadrangle to the QA-DT-P19 Cubic (QA-Cu4).

Coordinates:

1^st CT-coordinate:

p (q + r) (q² + r²) (2 p + q + r)

1^st DT-coordinate:

-p² + q² + r²

Properties:

– QA-P5.QA-P17

– QA-P10.QA-P16 (3 : -2 => QA-P19 = AntiCompl. of QA-P16 wrt QA-DT)

QA-P19 is the Reflection of QA-P5 in QA-P21.
QA-P19 is the Reflection of QA-P16 in QA-P31.
QA-P19 is the Involutary Conjugate (see QA-Tf2) of QA-P18. As a consequence the line QA-P18.QA-P19 is the common tangent of the circumscribed conics P1.P2.P3.P4.QA-P18 and P1.P2.P3.P4.QA-P19.
QA-P19 is the Isotomic Conjugate of QA-P20 wrt the QA-Diagonal Triangle.
QA-P19 is the Anticomplement of QA-P16 wrt the QA-Diagonal Triangle.
QA-P19 is the intersection of the tangents at QA-P5 and QA-P10 to the circumconic of the Reference Quadrangle that passes through QA-P5 and QA-P10 (note Randy Hutson).
QA-P19 lies on the Conic QA-Co5.
QA-P19 lies on the Cubic QA-Cu4.

MATHEMATICS