Quadrilateral \(ABCD \) is an isosceles trapezoid, with bases \(\overline{AB}\) and \(\overline{CD}.\) A circle is inscribed in the trapezoid, as shown below. (In other words, the circle is tangent to all the sides of the trapezoid.) The length of base \(\overline{AB}\) is \(2x\) and the length of base \(\overline{CD}\) is \(2y.\) Prove that the radius of the inscribed circle is \(\sqrt{xy}.\)
Heres the diagram:
https://latex.artofproblemsolving.com/0/5/c/05cb11f68ad87e7eaa5d910b04a6501e634a07e9.png
