7. The answer is (D). According to Thales' Theorem, the distance between the midpoints of the oblique sides is given by the semi-sum of the bases. Since the trapezoid is circumscribed around a circle, the sum of the bases is equal to the sum of the oblique sides. Since the trapezoid is a right trapezoid, the shorter oblique side is equal to the diameter of the inscribed circle, thus the answer is given by $\frac{20+24}{2}=22$.
7. A right trapezoid with the larger base $A B$ and the smaller base $C D$ is circumscribed around a circle with a radius of 10. It is known that the oblique side $\mathrm{BC}$ measures 24. What is the distance between the midpoints of $B C$ and $A D$?
(A) 21
(B) $\frac{13}{2} \sqrt{11}$
(C) $\frac{33}{5} \sqrt{11}$
(D) 22
(E) 23