# Prove that the tetragon ABCD also has an inscribed circle

There is given convex tetragon ABCD and some points J,K,L,M on the line segments AB,BC,CD,DA respectively. The intersection of JL and KM is T. Each of the tetragons AJTM,BKTJ,CLTK, and DMTL have an inscribed circle.

Prove that the tetragon ABCD also has an inscribed circle.