[obm-l] centro de semelhanca

["Luis Lopes" <llopes@xxxxxxxxxxxxx>]

Sauda,c~oes,

Mensagem recebida de uma outra lista:

Some months ago, I wrote:

>> I have read the following geometry problem marked
>> with "Iran, 1997":

>> Let ABC be a triangle and P a varying point on the arc
>> BC of the circumcircle of ABC. Prove that the circle
>> through P and the incenters of triangles PAB and PAC
>> passes through a fixed point independent of P.

> Later Jean-Pierre Ehrmann identfied this point as the
> intersection of the line AX(56) with the circumcircle,
> where X(56) is the external center of similtude of
> circumcircle and incircle.

> Remarkable: If P lies on the arc CA or on the arc AB,
> then the circle through P and the incenters of triangles
> PAB and PAC passes through A !

> Darij Grinberg

O que eh o centro externo de semelhanca? E o interno?
Como determiná-los?

[]'s
Luís


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