QA-Tr4: QL-P12-Triple Triangle

The QL-Centroids (QL-P12) of the 3 Quadrigons of the Reference Quadrangle form a triangle, which is the QL-P12-Triple Triangle.

For definition QL-Px-Triple Triangle see QA-1.

Area QL-P12-Triple Triangle in CT-notation:

2 p q r Δ / (18 (p + q) (p + r) (q + r))

Area QL-P12-Triple Triangle in DT-notation:

S / 18

Properties

• QA-Tr4 and QA-Tr1 are homothetic triangles. So both Euler lines are parallel.
• The Homothetic Center (Perspector) of QA-Tr1 and QA-Tr4 is QA-P43.
• Centroid QL-P12-Triple Triangle = QA-P26 = 2nd QA-Quasi Centroid.
• Circumcenter QL-P12-Triple Triangle lies on QA-P1.QA-P13.QA-P39.
• Orthocenter QL-P12-Triple Triangle is intersection point:
• QA-P1.QA-P11 ^ QA-P13.QA-P37 ^ the line // QA-P1.QA-P13 through QA-P10.
• The QL-Px-Triple Triangles of QL-P7, QL-P20, QL-P22, QL-P23 are all perspective with QA-Tr4. Their perspector is QA-P1 (QA-Centroid).
• The areas of these QL-Px-Triangles have ratios:
• QG-P1 : QL-P8 : QL-P12 : QL-P14 = 9 : 1 : 1/4 : 1/3.

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