IT-CESENATICO 2021 Problem 2

Let $ABC$ a triangle and let $I$ be the center of its inscribed circle. Let $D$ be the symmetric point of $I$ with respect to $AB$ and $E$ be the symmetric point of $I$ with respect to $AC$ . Show that the circumcircles of the triangles $BID$ and $CIE$ are eachother tangent.