Prove Lateral Sides Equal Midline in Inscribed Isosceles Trapezoid

A circle is inscribed in an isosceles trapezoid. Prove that the lengths of the lateral sides of the trapezoid are equal to the length of its midline.

Let the isosceles trapezoid be denoted as $ABCD$, where $AB$ and $CD$ are the parallel sides, with $AB < CD$. The midline $MN$ is defined as the line segment connecting the midpoints of the non-parallel sides $AD$ and $BC$. Show that the lengths of the lateral sides $AD$ and $BC$ are equal to the length of the midline $MN$.