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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

 Apr 4, 2021
 #1
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This is an easy application of Brahmagupta's formula.

 Apr 4, 2021
 #2
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What's that?

Guest Apr 6, 2021

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