The following problem is certainly appropriate for later in the year when geometry students reach this topic but it can also be used to review a considerable number of essential ideas in preparation for SATs, ACTs or just review in general. It's at the top end on the difficulty scale for these tests, but it's far from the AMC Contest!
Clarifications: Figures are not drawn to scale and the measure of ∠TAU is given in each diagram.
For each of the figures above, determine the following:
(a) the radius of each circle
(b) the length of minor arc TU in each circle
Have fun discovering a variety of approaches!
Variations? Generalizations? Choosing an angle other than special cases like 60 or 90 generally requires trig -- not that there's anything wrong with that!