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\(ABCD\) is a trapezium with \(AB < CD\) and \(AB\) parallel to \(CD\). \(\Gamma\) is a circle inscribed in \(ABCD\), such that \(\Gamma\) is tangent to all four sides. If \(AD = BC = 25 \) and the area of \(ABCD\) is \( 600\), what is the radius of \(\Gamma\)? 

 Jan 26, 2021
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Triangle AGD has an area of 150 square units.

 

Multiply 150 by 2, and divide the product by 25, and you'll have the radius.

 

 r = 300 / 25 = 12

 Jan 26, 2021
edited by jugoslav  Jan 26, 2021

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