10. The quadrilateral $A B C D$ is inscribed in a circle. It is known that the angle at $A$ is a right angle and that $\overline{A B}=24, \overline{B C}=20, \overline{C D}=15$. What is the measure of $D A$?
(A) 11
(B) 27
(C) 10
(D) 19
(E) 7
(10) The correct answer is $(E)$.

Since the angle at $A$ is a right angle, the diagonal $B D$ is a diameter and the angle at $C$ must also be a right angle. By the Pythagorean theorem in triangle $B C D$, we have $\overline{B D}=\sqrt{20^{2}+15^{2}}=25$. Therefore, by the Pythagorean theorem in triangle $B A D$, we have $\overline{D A}=\sqrt{25^{2}-24^{2}}=7$.

Question proposed by Carlo Cassola.