3. In an isosceles trapezoid, the bases are 9 cm and 21 cm, and the height is 8 cm. Find the radius of the circumscribed circle around the trapezoid.
3. Let's introduce a rectangular coordinate system as follows: the x-axis is directed to the right along the larger side of the trapezoid, point $O$ is chosen at the midpoint of the larger side, and the y-axis is directed perpendicular to the x-axis (see the figure).

![](https://cdn.mathpix.com/cropped/2024_05_06_33ef35229dd021a967afg-2.jpg?height=885&width=1356&top_left_y=366&top_left_x=476)

Denoting the vertices of the trapezoid by $A, B, C, D$, we get: $A(-10.5, 0)$, $B(10.5, 0)$, $C(4.5, 8)$, $D(-4.5, 8)$. Let point $E$ be the center of the desired circle. Then its coordinates will be $E(0, x)$. Applying the distance formula between two points and considering that $E C = E B = r$, we find $E C^2$ and $E B^2$: $E C^2 = 4.5^2 + (8 - x)^2$, $E B^2 = 10.5^2 + (0 - x)^2$. Equating the right-hand sides of these equations, we get $x = -1.625$. Then $r = E B = \sqrt{10.5^2 + 1.625^2} = 10.625$.

Remark. The problem can also be solved without the coordinate method.

Answer: $10.625$.