## Re: [EMHL] A simple triangle construction?..

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• ... Dear Luis, Yes it is. Your U_c = my W = pole of symmedian with respect to circumcircle = harmonic conjugate of T_c /AB This results into a construction
Message 1 of 10 , Jun 8, 2010
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Luís Lopes wrote:
>
> 1) [ to construct triangle ABC, given AB, angle A and foot T_c of
> symmedian ]
>
> Let t_c be the tangent to the circumcircle of ABC at C and U_c
> be the intersection (A,B)/\t_c.
>
> Trying to solve this problem I browsed a book of mine and read that
> H (U_c,A,T_c,B) are Harmonic conjugates. Then one can construct U_c.
>
> Would there be a construction based on this?
> I wonder whether U_c==W in <http://cjoint.com/?gioshSeBLy>
>

Dear Luis,

Yes it is.
Your U_c = my W = pole of symmedian with respect to circumcircle
= harmonic conjugate of T_c /AB

This results into a construction like :
Construct W = U_c = harmonic conjugate of T_c wrt AB
Then WC = tangent in C from W to circumcircle of ABC.
Thus a locus for C : circle with radius WC with WC^2 = WA.WB

The given construction is to draw W and this locus at once from a specific
easy constructed point "A" on this locus : point D.
(avoiding the separate effective constructions of harmonic conjugates,
and of radius from R^2 = WA.WB)

Regards.
Philippe
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