Desargues theorem for incenters. x(1127)

D - incenter of ABC incenters G,E,F are constructed for the triangles ABD, BCD, ACD accordingly. if J,I,H lie on a line, (and apparently that is always the case) applying the converse to Desargues theorem to triangles ABC и GEF it follows that AF, AE, CG intersect in the pont K. K = x(1127) I wonder what is known about line JIH ?