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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 $\sqrt{xy}.$

 Sep 30, 2020
 #1
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Here is the first part of the solution. Don't copy the words ditto-ditto, or you will get in trouble since this is a written proof, and you can be caught.

 

 Sep 30, 2020
 #2
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Wow, thanks, sorry, but I forgot to include that I want hints, not the full solution! Thanks anyways, and I'll be sure not to copy word by word (that would be plagiarism) but I will base my respose off yours!

Pangolin14  Sep 30, 2020

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