If you know one point and the equation of a circle, then the radius of this circle can be calculated.
Remember the general form of the equation of a circle equals,
h and k are the x and y coordinates of the center of the circle.
Example problem radius from equation of a circle.
Find the radius of a circle with an equation of (x-4)^2 + (y+3)^2 and contains (5,0)
(5-4)^2 + (0+3)^2 = r^2
1 +9 =r^2
√10 =radius (exact answer)
3.162 = radius (approximate answer)
Calculate Radius from the Diameter of the Circle
The distance around a circle is the circumference. If you measure the distance around a square, or rectangle it is called perimeter, but with a circle it is labeled as its circumference. Is circumference squared? No, it is a one dimensional measurement, and therefore is not squared. In order to help understand circumference, let’s review several properties of a circle. A circle can be named by its center point because all points of a circle are an equal distance from this center point. What is the circumference in terms of pi? Pi is calculated by dividing the circumference of a circle by the diameter of the same circle. It is approximately 3.14. The distance from the center of the circle to the edge of the circle is called radius. The circumference, diameter, and radius can all be used to calculate one another.
The term circumference is used often to describe spheres or circles. For example, what is the circumference of the earth? (24,901 miles) Bike tires, and basketballs are measured based on their circumference, but what is circumference?