Circles Packed Into A Trapezoid

If we feel inspired, and guess that the base has length $\boxed{21}$ and that the trapezium has height $8$ , then simple Pythagoras shows that two other sides have length $10$ , and that the two diagonals have length $17$ . The figure is full of $(6,8,10)$ and $(8,15,17)$ Pythagorean triads.

That a triangle with sides $9,10.17$ has inradius $2$ , and that a triangle with sides $10,17,21$ has inradius $3.5$ is easy to check.