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tangents

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Quadrilateral $$ABCD$$ is an isosceles trapezoid, with bases $$AB$$ and $$CD$$ 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 $$\overline{AB} = 2x$$ is  and the length of base $$\overline{CD} = 2y$$ is  Prove that the radius of the inscribed circle is $$\sqrt{xy}$$

May 5, 2021