Here is a simple problem which I would occasionally assign to my precalculus students and to my calculus students. The precalculus students always found a simpler answer. Sometimes it is possible to know too much. :)
Construct a simple proof that the area of the shaded region of the circle is $$ \frac{1}{2}\pi r^2+2ab $$
Caution! Mousing over the yellow region will reveal the answer.
Bonus: For those who got the answer or who revealed the answer, what does the dashed line represent? What is its equation?