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Angles in circles

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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:

Apr 4, 2021

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This is an easy application of Brahmagupta's formula.

Apr 4, 2021
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What's that?

Guest Apr 6, 2021