19672Re: [EMHL] ETC cyclic points
- Jan 5, 2011Dear Antreas,
> I think that the following search in ETC would beYes. It is not easy.
> interesting but I guess
> it is not easy!
>Yes. There are.
> Let (A), (B), (C) be three circles defined with known
> points listed in ETC
> such that they do not have a common KNOWN point.
> Not like these circles, for example:
> 1) 1 2 11 392
> 2) 1 2 23 36
> 3) 1 3 21 759
> Are there such circles which are concurrent?
In order to reduce the time of calculation by the
computer one of the three circles can be the
Hence one example is the circles
(O) (11, 13, 14), (36, 65, 79)
with common point P not in ETC and a second is
(O), (11, 13, 14), (46, 57, 79)
with the same common point P.
Hence we have found 4 circles concurrent at P.
(11, 13, 14) means the circle passing through
the two Fermat points X(13), X(14)
and the Feuerbach point X(11).
>I think that this point has not simple coordinates.
> If there are, then the point of concurrence is a NEW
> interesting point !
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