SHARYGIN 2020 Problem 24

Let $I$ be the incenter of a tetrahedron $ABCD$ , and $J$ be the center of the exsphere touching the face $BCD$ containing three remaining faces (outside these faces). The segment $IJ$ meets the circumsphere of the tetrahedron at point $K$ . Which of two segments $IJ$ and $JK$ is longer?