A trapezoid (,) is circumscribed. The incircle of the triangle touches the lines and at the points and ,respectively.Prove that the incenter of the trapezoid lies on the line .
A trapezoid $ABCD$ ($AB || CF$,$AB > CD$) is circumscribed. The incircle of the triangle $ABC$ touches the lines $AB$ and $AC$ at the points $M$ and $N$,respectively.Prove that the incenter of the trapezoid $ABCD$ lies on the line $MN$.
Školjka 
(
,
) is circumscribed. The incircle of the triangle 
touches the lines 
and 
at the points 
and 
,respectively.Prove that the incenter of the trapezoid 
.