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## 3 mixtilinear incircles have a common tangent

Problem (me): Given triangle $ABC$ with its circumcircle $(O)$. Let $L$ be an arbitrary point on arc $BC$ which does not contain $A$. Prove that the $A$-mixtilinear incircle of triangle $ABC$, $P$-mixtilinear incircles of triangles $PAB$ and $PAC$ have a common tangent.

Proof: See here