10,11

In a triangular pyramid $A B C D$, it is known that $A B=a$ and $\angle A C B=\angle A D B=90^{\circ}$. Find the radius of the sphere circumscribed around this pyramid.
Let $M$ be the midpoint of $AB$. Since in a right triangle the median drawn from the vertex of the right angle is equal to half the hypotenuse, then $MC = MA = MB = MD = 1/2 a$. Therefore, point $M$ is equidistant from each vertex of the given pyramid, with the distance being $1/2 a$. Consequently, $M$ is the center of the sphere circumscribed around the given pyramid, and the radius of the sphere is $1/2 a$.