Question 21
(TUR 2) Let $ABCD$ be a tetrahedron having each sum of opposite sides equal to 1. Prove that
$$r_A+r_B+r_C+r_D\le\frac{\sqrt3}{3},$$
where $r_A,r_B,r_C,r_D$ are the inradii of the faces, equality holding only if $ABCD$ is regular.
$$r_A+r_B+r_C+r_D\le\frac{\sqrt3}{3},$$
where $r_A,r_B,r_C,r_D$ are the inradii of the faces, equality holding only if $ABCD$ is regular.