The distance between two points $$P(6,0) \& Q(0,8)$$, which are situated at the two opposite ends of the circle C , will be the diameter of the circle.

So, the length of the diameter PQ is $$\sqrt{(6-0)^2+(0-8)^2}=\sqrt{36+64}=\sqrt{100}=10$$

$$Distance between points$ $$\left(x_1, y_1\right) \&\left(x_2, y_2\right)$$ is $$\left.\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$$

Thus, the radius of the circle is $$\frac{1}{2}($ Diameter $)=\frac{1}{2} \times 10=5$$

Hence the answer is (C).