HYACINTHOS 6560

In message #6539, I gave a list of the intersections of circles
depending on D. Here is a corrected (X(2) was wrong) and expanded
list:

|-------|------------------------------------------------|
| D | point of concurrence of the circles AB'C', |
| | A'BC', A'B'C, ABC |
|-------|------------------------------------------------|
| X(1) | X(100) = anticomplement of Feuerbach point = |
| | Feuerbach point of anticomplemetary triangle |
| X(2) | X(99) = Steiner point |
| X(3) | undefined (point jumping on circumcircle) |
| X(4) | X(107) |
| X(5) | X(110) = focus of Kiepert parabola = Feuerbach |
| | point of tangential triangle |
| X(6) | X(110) = focus of Kiepert parabola = Feuerbach |
| | point of tangential triangle |
| X(7) | not in ETC |
| X(8) | not in ETC |
| X(9) | X(100) = anticomplement of Feuerbach point = |
| | Feuerbach point of anticomplemetary triangle |
| X(10) | not in ETC |
| X(11) | X(104) = antipode of X(100); lies on ON, where |
| | O circumcenter and N Nagel point; lies on HF, |
| | where H orthocenter and F Feuerbach point. |
| X(12) | not in ETC |
| X(19) | not in ETC |
| X(20) | not in ETC |
| X(21) | not in ETC |
| X(23) | not in ETC |
| X(36) | not in ETC |
| X(37) | X(835) |
| X(39) | X(99) = Steiner point |
| X(63) | not in ETC |
|-------|------------------------------------------------|

Darij Grinberg