This question popped up in another thread and was answered there exactly. Let's see what geogebra can do.
AB and CD are two parallel chords in the same circle measuring 5 cm and 11 cm respectively.
If, the distance between AB and CD is 6 cm
Then find out the radius of the circle
1) Enter in the input box points (1,1),(12,1),(4,7),(9,7).
2) Use the rigid polygon tool and click points A,B,D and C to form a rigid polygon.
3) Go into the algebra pane and show points C and D.
You will notice that from the entered points you have two parallel line segments of length 11 and 5 and that they are 6 units away from each other.
4) Use the circle through three point tool and click A,C and D and a circle will appear, circumscribing the polygon.
5) Look in the algebra pane for the equation of that circle you will see
(x - 6.5)² + (y - 2)² = 31.25
6) Check that points A,B,C and D lie on the circle by plugging in.
7)Move the polygon and circle by dragging A or B. Since this is a rigid polygon it will remain invariant under the motion. Check the RHS of the equation of the circle. It will remain at 31.25 regardless of how we move or rotate the object.
Geogebra conjectures that
We are done!