# Geometry

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ABCD is a trapezoid 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?

• Geometry -

in a trapezoid like this the sum of two opposite sides is equal to the sum of the other two
thus the sum of the bases is 50

area = (1/2)(sum of the bases) x height
height = (2 area)/(sum of the bases)
height = 1200/50 = 24

height is also the diameter of the circle

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