5P-s-P5  5P-Schmidt Point


Consider a 5-Point (Pentangle) with vertices Pi (i=1,2,3,4,5).

Choose one of its vertices Pi.
Construct the perpendicular bisectors Lij of (Pi,Pj), where j unequal i.
In this way, Pi defines a 4-Line (Quadrilateral) formed by these perpendicular bisectors.
It appears that the Clawson-Schmidt Conjugate (QL-Tf1) wrt to this Quadrilateral of Pi is independent of the chosen Pi. This fixed point is 5P-s-P5.
This point was found by Eckart Schmidt. See Ref-34, QFG #3549.

5P s P5 Schmidt Point 02
 
Coordinates:
The coordinates are too complicated to mention here.

Properties:
• In a Triangle 5P-s-P5 of Pentangle ABCBr1Br2 (where Br1, Br2 are the 2 Brocard Points of Triangle ABC) is ETC Center X(98). See Ref-12.
• In a Reference Quadrilateral we have 3 Component Quadrigons (see QL-3QG1).
For each Component Quadrigon we can construct the circular cubic QA-Cu1.
These three cubics have 5 common points, which form a Pentangle extensively discussed in the Quadri-Figures Group, see Ref-34, keywords “3 QL-versions of QA-Cu7” and “5P-Geometry”.
The point 5P-s-P5 of this Pentangle coincides with a point U, being the intersection point of the 3 QL-versions of QA-P41.QG-P18 of the Reference Quadrilateral.