Question #N1026
In the $xy$-plane, a circle with center $(3,2)$ passes through the point $(7,6)$. What is the radius of the circle?
A. 4
B. 5
C. 8
D. 13
Correct Answer is: B
The radius of the circle is the distance between the center of the circle and any point on the circle. We can use the distance formula to find this distance: \begin{align*} \sqrt{(7-3)^2 + (6-2)^2} &= \sqrt{4^2 + 4^2} \\ &= \sqrt{16 + 16} \\ &= \sqrt{32} \\ &= 4\sqrt{2} \\ &= 4(\sqrt{2 * 2}) \\ &= 4(\sqrt{2})(\sqrt{2}) \\ &= 4(2) \\ &= 8. \end{align*} The radius of the circle is 8, so the correct answer is B.