MathNet 2009-part-03 — 175 problems (EN–VI) Question 77

A circle of radius $2~\mathrm{cm}$ is inscribed in $\triangle ABC$. Let $D$ and $E$ be the points of tangency of the circle with the sides $AC$ and $AB$, respectively. If $\angle BAC = 45^\circ$, find the length of the minor arc $DE$.