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# geometry problem. help requested :(

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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

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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