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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
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When x = y, ABCD is a square with side length 2x, and the radius is x.

 May 5, 2021

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