Problem - 3109
As shown, two vertices of a square are on the circle and one side is tangent to the circle. If the side length of the square is 8, find the radius of the circle.
Let the circle's radius be $r$. Draw a diameter that is perpendicular to the bottom side. Then $$(2r-8)\times 8 = 4\times 4\implies r=\boxed{5}$$
