QA-P12: Orthocenter of the QA-Diagonal Triangle

QA-P12 is the Orthocenter of the Diagonal Triangle (QA-Tr1) of a Quadrangle.
 QA-P12-Orthocenter-DT-00
                       
Coordinates: 
1st CT-Coordinate:
                (2 SA p2 q r + TA) (a2 q r + SB p q + SC p r) , 
where:
                TA = -a2 q2 r2 + b2 p2 r2 + c2 p2 q2
 
1st DT-Coordinate:
                 SB SC
 
Properties:
  • QA-P12 lies on these QA-lines:
        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)