MathDB

One triangular face

F

of a tetrahedron

\mathcal{T}

has side lengths

\sqrt{5}

\sqrt{65}

, and

2\sqrt{17}

. The other three faces of

\mathcal{T}

are right triangles whose hypotenuses coincide with the sides of

F

. There exists a sphere inside

\mathcal{T}

tangent to all four of its faces. Compute the radius of this sphere.

Problem Statement