How to Find the Radius of a Circle With the Midpoint

By Chance E. Gartneer

The midpoint of a line is the halfway mark of that line. A radius measures the distance from a circle's middle point, or origin, to its surrounding perimeter, also known as its circumference. The midpoint has much in common with the radius, for the midpoint on a diameter measures its corresponding radius since the diameter's length is twice that of its radius. You can find the radius of a circle from the coordinates of its diameter's midpoint and the coordinates of a point on its circumference.

Step 1

Subtract the x-coordinate of the point on the circumference from the x-coordinate of the midpoint, and then square the difference. For example, the point on the circumference is (3,4) and the midpoint is (7,7). Subtracting the circumference point's x-coordinate with a value of 3 from the midpoint's x-coordinate with a value of 7 results in 4. The square of 4 is 16.

Step 2

Subtract the y-coordinate of the point on the circumference from the y-coordinate of the midpoint and then square the difference. For this example, subtracting the circumference point's y-coordinate with a value of 4 from the midpoint's y-coordinate with a value of 7 results in 3, and 3 squared is 9.

Step 3

Add the squares from steps 1 and 2 together and then calculate the square root of that sum to calculate the length of the radius. For this example, 9 added to 16 equals 25, and the square root of 25 is 5. The length of the radius is 5.

About the Author

Chance E. Gartneer began writing professionally in 2008 working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.