Theorem:
The circles (167), (275) and (356) concur at a point (say) 8.
Special Cases:
1. Let the points 4,5,6,7 be concyclic (or collinear). See previous post.
2. Let the points 5,6,7 be the second intersections [= other than the point 4] of the lines 14, 24, 34 with the circles (423),(431),(412) resp.
3. Let the points 5,6,7 be the second intersections [= other than the point 4] of the circles (1,14),(2,24),(3,34) with the circles (423),(431), (412) resp.
4. Let 1',2',3' be the centers of the circles (423),(431),(412), resp. and the points 5,6,7, the second intersections [= other than the point 4] of the circles (42'3'),(43'1'),(41'2') with the circles (423),(431),(412) resp.
Continued 5
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