examday

/TMUA

In trapezium $ABCD$, the sides $AB$ and $DC$ are parallel, and $AD$ is perpendicular to them. Also, $AB=9$ and $DC=4$. A circle lies inside the trapezium and is tangent to all four sides, as shown.

What is the radius of the circle?

You may use the fact that the two tangent segments from an external point to a circle have equal lengths.