QG-P17: Projection QG-P1 on QG-L1

QG-P17: Projection Point of QG-P1 on QG-L1

QG-P17 is the projection of QG-P1 on QG-L1.

This point and its properties were found by Eckart Schmidt (October 5, 2012).

Coordinates:

CT-Coordinates in 1^st QA-Quadrigon:

(-p (c² p² q (q + r) + r (b² p² (q + r) - a² q (p² + q r))) : p q r (a² q (p - r) + c² q (-p + r) - b² (p q + 2 p r + q r)) : (-p - q) (b² p + a² q) r³ + c² p q r (p q + r²))

DT-Coordinates in 1^st QA-Quadrigon:

CT-Coordinates in 1^st QL-Quadrigon:

(m n (a² l² - c² n²) : l n (a² (l - m) (l - n) + c² (l - n) (m - n) - b² (l m - l n + m n)) : -l m(a² l² - c² n²))

DT-Coordinates in 1^st QL-Quadrigon:

Properties:

– QG-P1.QL-P10.QA-P12

– QG-P2.QG-P3 (=QG-L1)

QG-P17 lies on the medial circles QA-Ci2 and QL-Ci2.
The 3 QL-versions of QG-P17 are the vertices of the Orthic Triangle of the QL-Diagonal Triangle (QL-Tr1) and lie on QA-Cu7.
QG-P17 is the second focus of an inscribed conic with its first focus in QG-P18.
QG-P17 is the QL-Tf1 image of QG-P18.
The Polar (see Ref-13, Polar) of QG-P17 wrt any inscribed or circumscribed conic of the Reference Quadrigon is a line through QG-P1.
The QA-Orthopole (QA-Tf3) of QG-P17 is the Midpoint (QG-P1.QG-P18).
QG-P17.QG-P1 is the Angle Bisector of angles P1.QG-P17.P3 and P2.QG-P17.P4.
The Triple Triangle of QG-P17 is perspective with all QA-Component Triangles (see QA-Tr-1 for Desmic Triple Triangles).

MATHEMATICS