<p>An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is <img alt="$3$" height="12" src="https://latex.artofproblemsolving.com/7/c/d/7cde695f2e4542fd01f860a89189f47a27143b66.png" width="8" />, and the area of the trapezoid is <img alt="$72$" height="12" src="https://latex.artofproblemsolving.com/9/4/d/94db15b430439ad5b3c80bfacfef0c6499ede2ee.png" width="17" />. Let the parallel sides of the trapezoid have lengths <img alt="$r$" height="8" src="https://latex.artofproblemsolving.com/b/5/5/b55ca7a0aa88ab7d58f4fc035317fdac39b17861.png" width="8" /> and <img alt="$s$" height="8" src="https://latex.artofproblemsolving.com/f/3/7/f37bba504894945c07a32f5496d74299a37aa51c.png" width="8" />, with <img alt="$r \neq s$" height="18" src="https://latex.artofproblemsolving.com/1/0/8/108b5fe90572221ce15300e946f49a14c093e090.png" width="43" />. Find <img alt="$r^2+s^2$" height="16" src="https://latex.artofproblemsolving.com/0/7/6/07650f34c1a265622f7d8bd3d56c269fe2cef73e.png" width="53" /></p>

Question No: 404

An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is $3$ , and the area of the trapezoid is $72$ . Let the parallel sides of the trapezoid have lengths $r$ and $s$ , with $r \neq s$ . Find $r^2+s^2$

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Tags: Geometry

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