## Re: [EMHL] excentral triangle as tangents to ellipses

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• Dear Nikos, Of course, this makes perfect sense now.  Thanks! Randy ... [Non-text portions of this message have been removed]
Message 1 of 4 , Jul 31, 2012
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Dear Nikos,

Of course, this makes perfect sense now.  Thanks!

Randy

>________________________________
>To: Hyacinthos@yahoogroups.com
>Sent: Tuesday, July 31, 2012 12:42 AM
>Subject: Re: [EMHL] excentral triangle as tangents to ellipses
>
>Dear Randy
>I think that are known
>because if F, F' are the foci
>of an ellipse and P a point on it
>then the tangent at P to the ellipse
>is perpendicular to the internal bisector PQ
>of triangle PFF' at P.
>In case of an hyperbola the tangent is the line PQ.
>Best regards
>
>> Are these known results?
>>
>> 1) Let Ea be the ellipse with B and C as foci and passing
>> through A.  Define Eb, Ec cyclically.  Let La be
>> the tangent to Ea at A, and define Lb, Lc cyclically.
>> The lines La, Lb, Lc form the excentral triangle.
>>
>> 2) Let A', B', C' be points on segments BC, CA, AB
>> respectively.  Let Ea be the ellipse with B' and C' as
>> foci and passing through A, and define Eb, Ec
>> cyclically.  Let La be the tangent to Ea at A, and
>> define Lb, Lc cyclically.  The lines La, Lb, Lc form
>> the excentral triangle.
>>
>> 3) Let P and P' be isogonal conjugates both inside
>> ABC.  Let Ea be the ellipse with P and P' as foci and
>> passing through A, and define Eb, Ec cyclically.  Let
>> La be the tangent to Ea at A, and define Lb, Lc
>> cyclically.  The lines La, Lb, Lc form the excentral
>> triangle.
>>
>> Thank you,
>> Randy Hutson
>>
>>
>>
>> ------------------------------------
>>
>>
>>
>>     Hyacinthos-fullfeatured@yahoogroups.com
>>
>>
>
>
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>