Dear Mathlinkers, if I have understand your problem, the point of concur is the incenter of the triangle determined by the three points... Sincerely Jean-Louis

jayme wrote: Dear Mathlinkers, if I have understand your problem, the point of concur is the incenter of the triangle determined by the three points... Sincerely Jean-Louis This comes from the following lemma: Lemma: Let $I,E$ be the incenter and the $A$-excenter of $\triangle ABC$, respectively. Let $D$ be the midpoint of the arc $BC$ of circle $ABC$ which doesn't contain $A$. Then, $DB=DC=DI=DE$. Also, Lemma: Let $F,G$ be the $B$-excenter and the $C$-excenter of $\triangle ABC$, respectively. Let $M$ be the midpoint of the arc $BC$ of circle $ABC$ which contains $A$. Then, $MB=MC=MF=MG$. Both the lemmas can be proved by trivial angle chasing.

Dear Mathlinkers, yes, your lemma is well known... it comes from Mention, a French geometer of the past... Sincerely Jean-Louis