QA-P12: Orthocenter QA-Diag.Triangle

QA-P12: Orthocenter of the QA-Diagonal Triangle

QA-P12 is the Orthocenter of the Diagonal Triangle (QA-Tr1) of a Quadrangle.

Coordinates:

1st CT-Coordinate:

(2 S_A p² q r + T_A) (a² q r + S_B p q + S_C p r) ,

where:

T_A = -a² q² r² + b² p² r² + c² p² q²

1st DT-Coordinate:

S_B S_C

Properties:

– QA-P1.QA-P37 ( -1 : 2 => QA-P12 is Reflection of QA-P37 in QA-P1)

– QA-P2.QA-P36 ( 2 : -1 => QA-P12 is Reflection of QA-P2 in QA-P36)

– QA-P10.QA-P11 (-2 : 3)

– QA-P14.QA-P33 (-2 : 3)

– QA-P29.QA-P30 (-1 : 2 => QA-P12 is Reflection of QA-P30 in QA-P29)

QA-P12 is the QA-Involutary Conjugate (see QA-Tf2) of QA-P23.
QA-P12 is the Antipode of QA-P30 in the QA-DT-P3-P12 Orthogonal Hyperbola (QA-Co4).
QA-P12 is the Isotomic Center (QA-P5) of the Circumcenter Quadrangle (Eckart Schmidt, August 24, 2012).
QA-P11 is the QA-Orthopole (QA-Tf3) of QA-P12.
QA-P12 is the Orthology Center of the QG-P1 Triple Triangle wrt the Triple triangles of QG-P2/QG-P4/QG-P8/QG-P15/QL-P10/QL-P12. See QA-Tr-1.
QA-P12 is the Orthology Center of the QG-P17 Triple Triangle wrt the Triple triangles of QG-P1/QG-P2/QG-P4/QG-P8/QG-P15/QL-P12. See QA-Tr-1.
QA-P12 is the Orthology Center of the QL-P10 Triple Triangle wrt the Triple triangles of QG-P2/QG-P4/QG-P8/QG-P15/QL-P12. See QA-Tr-1.

MATHEMATICS