## Task A-3.4.

Let $A B C D$ be a tetrahedron where $\varangle B A C=\varangle C A D=\varangle D A B=90^{\circ}$, $|A D|=2 \sqrt{2}$, and $|A B|=|A C|=3$. Determine the radius of the sphere inscribed in this tetrahedron.