How to find center and radius of a circle?

Let’s find center and radius of a circle. There is no definitive answer to this question as it depends on the particular method being used. However, some common methods for finding the center and radius of a circle include using a compass or ruler to draw a diameter of the circle and then using a ruler or tape measure to find the distance from the center to the edge of the circle. Additionally, the center and radius can also be found by graphing the equation of the circle.

How to find center and radius of a circle?

The center of a circle is the point equidistant from all points on the circle. The radius of a circle is the distance from the center of the circle to any point on the circle.

Step-by-step examples of finding the center and radius of circles

  • Find the center and radius of the circle with the equation x^2 + y^2 = 9.

The center of the circle is at (0, 0). The radius is 3.

  • Find the center and radius of the circle with equation (x – 4)^2 + (y + 3)^2 = 25.

The center of the circle is at (4, -3). The radius is 5.

  • Find the center and radius of the circle with equation (x – 2)^2 + (y – 5)^2 = 9.

The center of the circle is at (2, 5). The radius is 3.

  • Find the center and radius of the circle with equation (x + 1)^2 + (y – 4)^2 = 16.

The center of the circle is at (-1, 4). The radius is 4.

There are a few ways to find the center and radius of a circle:

  • Use a compass or ruler to draw a diameter of the circle. Then, use a ruler or tape measure to find the distance from the center to the edge of the circle.
  • Use the equation of the circle. The center of the circle is at the point (h, k), and the radius is r.
  • Graph the equation of the circle. The center of the circle is at the intersection of the x-axis and the y-axis, and the radius is the distance from the center to any point in the circle.
  • Use the Pythagorean Theorem. If the circle is centered at the origin, the radius is the square root of the sum of the squares of the x-coordinate and the y-coordinate of any point on the circle.
  • Use the distance formula. The radius is the distance from the center of the circle to any point on the circle.

Example

To find the center, draw a line from any point on the circle to the midpoint of the circle. The intersection of this line and the x-axis is the center of the circle.

To find the radius, use the Pythagorean Theorem. If the circle is centered at the origin, the radius is the square root of the sum of the squares of the x-coordinate and the y-coordinate of any point on the circle. In this case, the radius is the square root of the sum of the squares of 4 and 3, which is 5.

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