QA-Tr-3: (Quadri-)Orthologic QA-Triple Triangles


Two triangles A1B1C1 and A2B2C2 are Orthologic if the perpendiculars from the vertices A1, B1, C1 on the sides B2C2, A2C2, and A2B2 are concurrent.

The point of concurrence is known as the Orthology Center of A1B1C1 with respect to A2B2C2.

If this is the case, then the perpendiculars from the vertices A2, B2, C2 on the sides B1C1, A1C1, and A1B1 are also concurrent, as shown by Steiner in 1827. See [13], Orthologic Triangles. The point of concurrence is known as the Orthology Center of A2B2C2 with respect to A1B1C1.

Here is a list of Orthologic pairs of Triple Triangles in a Quadrangle.

Triple Triangle-1
formed by 3
QA-versions of:
Triple Triangle-2
formed by 3
QA-versions of:
Orthology Center-1 Orthology Center-2
QG-P1 QG-P2 QA-P12 QA-P11
QG-P1 QG-P4 QA-P12 QA-Px
QG-P1 QG-P5 QA-P20 QA-Px
QG-P1 QG-P6 QA-Px QA-P24
QG-P1 QG-P7 QA-P3 QA-Px
QG-P1 QG-P8 QA-P12 QA-Px
QG-P1 QG-P9 QA-P3 QA-P32
QG-P1 QG-P10 QA-P20 QA-Px
QG-P1 QG-P11 QA-Px QA-Px
QG-P1 QG-P15 QA-P12 QA-P37
QG-P1 QG-P17 QA-P11 QA-P12
QG-P1 QL-P2 QA-P20 QA-Px
QG-P1 QL-P6 QA-P3 QA-Px
QG-P1 QL-P10 QA-Px QA-P12
QG-P1 QL-P12 QA-P12 QA-Px
QG-P2 QG-P4 QA-P11 QA-Px
QG-P2 QG-P5 QA-P1 QA-Px
QG-P2 QG-P6 QA-Px QA-P24
QG-P2 QG-P7 QA-Px QA-Px
QG-P2 QG-P8 QA-P11 QA-Px
QG-P2 QG-P9 QA-Px QA-P32
QG-P2 QG-P10 QA-P1 QA-Px
QG-P2 QG-P11 QA-Px QA-Px
QG-P2 QG-P15 QA-P11 QA-P37
QG-P2 QG-P17 QA-P13 QA-P12
QG-P2 QL-P2 QA-P1 QA-Px
QG-P2 QL-P6 QA-Px QA-Px
QG-P2 QL-P10 QA-Px QA-P12
QG-P2 QL-P12 QA-P11 QA-Px
QG-P3 QL-P5 QA-Px QA-Px
QG-P3 QL-P15 QA-Px QA-Px
QG-P3 QL-P18 QA-Px QA-Px
QG-P4 QG-P5 QA-Px QA-Px
QG-P4 QG-P6 QA-Px QA-P24
QG-P4 QG-P7 QA-Px QA-Px
QG-P4 QG-P8 QA-Px QA-Px
QG-P4 QG-P9 QA-Px QA-P32
QG-P4 QG-P10 QA-Px QA-Px
QG-P4 QG-P11 QA-Px QA-Px
QG-P4 QG-P15 QA-Px QA-P37
QG-P4 QG-P17 QA-Px QA-P12
QG-P4 QL-P2 QA-Px QA-Px
QG-P4 QL-P6 QA-Px QA-Px
QG-P4 QL-P10 QA-Px QA-P12
QG-P4 QL-P12 QA-Px QA-Px
QG-P5 QG-P6 QA-Px QA-Px
QG-P5 QG-P7 QA-Px QA-Px
QG-P5 QG-P8 QA-Px QA-P10
QG-P5 QG-P9 QA-Px QA-Px
QG-P5 QG-P10 QA-Px QA-Px
QG-P5 QG-P11 QA-Px QA-Px
QG-P5 QG-P12 QA-P32 QA-P1
QG-P5 QG-P14 QA-P32 QA-P5
QG-P5 QG-P15 QA-Px QA-P5
QG-P5 QL-P2 QA-Px QA-P15
QG-P5 QL-P3 QA-Px QA-P15
QG-P5 QL-P4 QA-P9 QA-Px
QG-P5 QL-P5 QA-Px QA-P1
QG-P5 QL-P6 QA-Px QA-Px
QG-P5 QL-P7 QA-Px QA-P1
QG-P5 QL-P12 QA-Px QA-P1
QG-P5 QL-P20 QA-Px QA-P1
QG-P5 QL-P22 QA-Px QA-P1
QG-P5 QL-P23 QA-Px QA-P1
QG-P5 QL-P27 QA-Px QA-Px
QG-P5 QL-P29 QA-Px QA-P15
QG-P5 QL-P30 QA-Px QA-Px
QG-P5 All Component Triangles (QA-4Tr1) Quadri-Orthologic Quadri-Orthologic
QG-P6 QG-P7 QA-Px QA-Px
QG-P6 QG-P8 QA-P24 QA-Px
QG-P6 QG-P9 QA-Px QA-Px
QG-P6 QG-P10 QA-Px QA-Px
QG-P6 QG-P11 QA-Px QA-Px
QG-P6 QG-P15 QA-P24 QA-Px
QG-P6 QL-P2 QA-Px QA-Px
QG-P6 QL-P6 QA-Px QA-Px
QG-P6 QL-P12 QA-P24 QA-Px
QG-P7 QG-P8 QA-Px QA-P34
QG-P7 QG-P9 QA-P15 QA-Px
QG-P7 QG-P10 QA-Px QA-Px
QG-P7 QG-P11 QA-Px QA-Px
QG-P7 QG-P15 QA-Px QA-P2
QG-P7 QL-P1 QA-Px QA-P3
QG-P7 QL-P2 QA-Px QA-Px
QG-P7 QL-P6 QA-P15 QA-Px
QG-P7 QL-P12 QA-Px QA-Px
QG-P8 QG-P9 QA-P34 QA-P32
QG-P8 QG-P10 QA-P10 QA-Px
QG-P8 QG-P11 QA-Px QA-Px
QG-P8 QG-P15 QA-Px QA-P37
QG-P8 QG-P17 QA-Px QA-P12
QG-P8 QL-P2 QA-P10 QA-Px
QG-P8 QL-P6 QA-P34 QA-Px
QG-P8 QL-P10 QA-Px QA-P12
QG-P8 QL-P12 QA-Px QA-Px
QG-P9 QG-P10 QA-Px QA-Px
QG-P9 QG-P11 QA-Px QA-Px
QG-P9 QG-P15 QA-P32 QA-P2
QG-P9 QL-P1 QA-Px QA-P3
QG-P9 QL-P2 QA-Px QA-Px
QG-P9 QL-P6 QA-Px QA-Px
QG-P9 QL-P12 QA-P32 QA-Px
QG-P10 QG-P11 QA-Px QA-Px
QG-P10 QG-P12 QA-Px QA-P1
QG-P10 QG-P14 QA-Px QA-P5
QG-P10 QG-P15 QA-Px QA-P5
QG-P10 QL-P2 QA-Px QA-P15
QG-P10 QL-P3 QA-Px QA-P15
QG-P10 QL-P4 QA-Px QA-Px
QG-P10 QL-P5 QA-Px QA-P1
QG-P10 QL-P6 QA-Px QA-Px
QG-P10 QL-P7 QA-Px QA-P1
QG-P10 QL-P12 QA-Px QA-P1
QG-P10 QL-P20 QA-Px QA-P1
QG-P10 QL-P22 QA-Px QA-P1
QG-P10 QL-P23 QA-Px QA-P1
QG-P10 QL-P27 QA-Px QA-Px
QG-P10 QL-P29 QA-Px QA-P15
QG-P10 QL-P30 QA-Px QA-Px
QG-P10 All Component Triangles (QA-4Tr1) Quadri-Orthologic Quadri-Orthologic
QG-P11 QG-P15 QA-Px QA-Px
QG-P11 QL-P2 QA-Px QA-Px
QG-P11 QL-P6 QA-Px QA-Px
QG-P11 QL-P12 QA-Px QA-Px
QG-P12 QG-P14 QA-Px QA-Px
QG-P12 QL-P2 QA-P1 QA-Px
QG-P14 QL-P2 QA-P5 QA-Px
QG-P15 QG-P17 QA-Px QA-P12
QG-P15 QL-P2 QA-P5 QA-Px
QG-P15 QL-P6 QA-P2 QA-Px
QG-P15 QL-P10 QA-Px QA-P12
QG-P15 QL-P12 QA-P37 QA-Px
QG-P17 QG-P18 QA-Px QA-P23
QG-P17 QL-P12 QA-P12 QA-Px
QL-P1 QL-P6 QA-P3 QA-Px
QL-P2 QL-P3 QA-Px QA-P15
QL-P2 QL-P4 QA-Px QA-Px
QL-P2 QL-P5 QA-Px QA-P1
QL-P2 QL-P6 QA-Px QA-Px
QL-P2 QL-P7 QA-Px QA-P1
QL-P2 QL-P12 QA-Px QA-P1
QL-P2 QL-P20 QA-Px QA-P1
QL-P2 QL-P22 QA-Px QA-P1
QL-P2 QL-P23 QA-Px QA-P1
QL-P2 QL-P27 QA-Px QA-Px
QL-P2 QL-P29 QA-Px QA-P15
QL-P2 QL-P30 QA-Px QA-Px
QL-P2 All Component Triangles (QA-4Tr1) Quadri-Orthologic Quadri-Orthologic
QL-P3 QL-P29 QA-Px QA-Px
QL-P4 QL-P22 QA-Px QA-Px
QL-P4 QL-P30 QA-Px QA-Px
QL-P5 QL-P15 QA-Px QA-Px
QL-P5 QL-P18 QA-Px QA-Px
QL-P6 QL-P12 QA-Px QA-Px
QL-P10 QL-P12 QA-P12 QA-Px
QL-P10 QL-P23 QA-Px QA-Px
QL-P15 QL-P18 QA-Px QA-Px
QL-P22 QL-P30 QA-Px QA-Px

QA-Px is a QA-point not registered in EQF.




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