Circle Inscribed in a Trapezium

Geometry Level 3

$ABCD$ 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 $\Gamma$ ?