Question #N352
A circle has a radius of 5 units and a diameter with endpoints (2, 4) and (2, 14). An equation of this circle is $(x - h)^2 + (y - k)^2 = r^2$, where r is a positive constant. What is the value of r?
A. 2
B. 5
C. 10
D. 25
Correct Answer is: B
The radius of a circle is the distance from the center of the circle to any point on the circle. Since the endpoints of a diameter are given, the length of the diameter is the distance between those two points. The distance between (2, 4) and (2, 14) is 10. Since the radius is half the diameter, the radius is 5. In the equation of the circle, r represents the radius, so r = 5.