MathNet 2025-part-01 — 187 problems (EN–VI) Question 54

The incentre of a triangle $ABC$ is $I$. Points $D$ and $E$ on the sides $AB$ and $AC$, respectively, satisfy $DI \perp BI$ and $EI \perp CI$. Prove that the line $DE$ is tangent to the incircle of the triangle $ABC$.