QA-P27: M3D Center

QA-P27 is the perspector of the QA-Diagonal Triangle and the QA-M3D Triangle.

The QA-M3D Triangle (Ma.Mb.Mc in the figure) is the triangle bounded by the M3D Lines (see paragraph QL-L9) occurring in the 3 QA-Quadrigons.

1st CT-Coordinate

(q + r) (2 p + q + r) (q² + q r + r²)

(-p⁴ – 2 p³ q – 2 p² q² – p q³ – 2 p³ r + p q² r + q³ r – 2 p² r² + p q r² + q² r² – p r³ + q r³)

1st DT-Coordinate

1/((p² + q² + r²)² – 4 ((q² + r²)² – q² r²))

Area of M3D Triangle (CT-coordinates):

2 Δ (p² + p q + q² + p r + q r + r²)² / (3 (p + q) (p + r) (q + r) (p + q + r))

Properties

• QA-P27 lies on the line through QA-P10 parallel to QA-P5.QA-P17.
• QA-P27 is the Involutary Conjugate (see QA-Tf2) of QA-P21.

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