let $ABC$ be a triangle and $I$ be its incentre. let the incircle of $ABC$ touch $BC$ at $D$. let incircle of triangle $ABD$ touch $AB$ at $E$ and incircle of triangle $ACD$ touch $AC$ at $F$. prove that $B,E,I,F$ are concyclic.
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Tags: geometry, geometry unsolved
let $ABC$ be a triangle and $I$ be its incentre. let the incircle of $ABC$ touch $BC$ at $D$. let incircle of triangle $ABD$ touch $AB$ at $E$ and incircle of triangle $ACD$ touch $AC$ at $F$. prove that $B,E,I,F$ are concyclic.