How to Find the Radius of a Circle With the Midpoint

The circle's circumference relates to its radius.
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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.

    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.

    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.

    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.

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