MathNet 2015-part-02 — 191 problems (EN–VI) Question 14

Let $ABCD$ be a tetrahedron such that $\angle BAC = \angle CAD = \angle DAB = 90^\circ$, $|AD| = 2\sqrt{2}$ and $|AB| = |AC| = 3$ holds. Determine the radius of the inscribed sphere of the tetrahedron. (Mea Bombardelli)