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Let \(ABCD\) be 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 \(\sqrt{xy}.\)
 

 

Here's the image:

 

Thanks!

 Apr 4, 2020
 #1
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If ABCD is a square, then x = y, and the radius is sqrt(x*y) = x, so the formula works.

 Apr 4, 2020
 #2
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This was posted by me. It is in algebraic proof.

 Apr 5, 2020

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