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X(5394) CONGRUENT INCIRCLES POINT seems not to be unique

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• Dear geometers: I have found numerically at least other three points determining congruent incircles as in X(5394). In the SEARCH triangle (6,9,13): Pa:
Message 1 of 2 , Jan 12, 2013
Dear geometers:

I have found numerically at least other three points determining congruent
incircles as in X(5394).

In the SEARCH triangle (6,9,13):

Pa: (u,v,w)=( -2.5886025937.., 3.4499648937.., 2.4469669068..) ,

Pb: (u,v,w)=( 6.009055300265.., -2.894577976679.., 2.871192942765..),

Pc: (u,v,w)=) 9.637881480452.., 6.105715434464.., -5.034622271032..),

Note that each of these points is outside the triangle.

The given X(5394) has (u,v,w)=( 1.791642688432.., 1.705729272515..,
1.632862975866..), inradius=0.803384896397 This point is interior to ABC.
IMHO, X(5394) should be specified that it is an interior point of the
triangle.

Id like to check the work by Noam Elkies in Mathematics Magazine 60 (1987)
117, cited by ETC in X(5394) and proving the existence of this point.
Anybody can share it with me?

[Non-text portions of this message have been removed]
• Dear César, Could Pa, Pb, Pc be extraversions of X(5394)?  I also wondered if PaPbPc might be perspective to ABC, but this turns out not to be the case.
Message 2 of 2 , Jan 14, 2013
Dear César,

Could Pa, Pb, Pc be extraversions of X(5394)?  I also wondered if PaPbPc might be perspective to ABC, but this turns out not to be the case.

Randy

>________________________________
>To: Hyacinthos@yahoogroups.com
>Sent: Saturday, January 12, 2013 8:24 PM
>Subject: [EMHL]4X(539) CONGRUENT INCIRCLES POINT seems not to be unique
>
>

>Dear geometers:
>
>I have found numerically at least other three points determining congruent
>incircles as in X(5394).
>
>In the SEARCH triangle (6,9,13):
>
>Pa: (u,v,w)=( -2.5886025937.., 3.4499648937.., 2.4469669068..) ,
>
>Pb: (u,v,w)=( 6.009055300265.., -2.894577976679.., 2.871192942765..),
>
>Pc: (u,v,w)=) 9.637881480452.., 6.105715434464.., -5.034622271032..),
>
>Note that each of these points is outside the triangle.
>
>The given X(5394) has (u,v,w)=( 1.791642688432.., 1.705729272515..,
>1.632862975866..), inradius=0.803384896397… This point is interior to ABC.
>IMHO, X(5394) should be specified that it is an interior point of the
>triangle.
>
>I’d like to check the work by Noam Elkies in Mathematics Magazine 60 (1987)
>117, cited by ETC in X(5394) and proving the existence of this point.
>Anybody can share it with me?
>