Re: Geometry Problem

Hi,

OwlHoot wrote:
Bractals wrote:

Let P and Q be the circumcircle and incircle respectively of an arbitrary triangle.
If ABC is a triangle inscribed in P with AB and AC tangent to Q, then BC is
tangent to Q.
[...]
>
all six vertices of the two triangles are distinct and in
order round the circumcircle they form vertices of a hexagon,
> which suggests that Pascal's Theorem may be relevant: [...]

But two distinct triangles don't make *one* single hexagon !

BTW, looking for some stuff, I found there must be some mistake there,
Mathworld says in :
http://mathworld.wolfram.com/PonceletsPorism.html

[1]
> For [...] an odd-sided polygon, the lines connecting the
> vertices to the opposite points of tangency are concurrent
> at the limiting point [of the two circles].

That is for any triangle, the Gergonne point is the limiting
point of the Incircle and the Circumcircle ?????
That would pretend that incenter, circumcenter and Gergonne
point are in line, what they are not.
(I agree with the ETC list of lines and centers,
for X(1), X(3) and X(7) not in line)

Seems that statement [1] is wrong...
(the part "at the limiting point" : this intersection point
is not a fixed point when triangle "rotates" in the porism.)

Regards.
--
Philippe C.
chephip+news@xxxxxxx

.

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