Content

• To step
• Method 1 of 3: Calculate the radius if you know the diameter
• Method 2 of 3: Calculate the radius if you know the circumference
• Method 3 of 3: Calculate the radius if you know the coordinates of three points on the circle

The radius of a circle is the distance from the center of the circle to the edge. The diameter of a circle is the length of the straight line that can be drawn between two points on the sphere or circle and through its center. You are often asked to calculate the radius of a circle based on other data. In this article, you will learn how to calculate the radius of a circle based on a given diameter, circumference and area. The fourth method is a more advanced method of determining the center and radius of a circle based on the coordinates of three points on the circle.

To step

Method 1 of 3: Calculate the radius if you know the diameter

1. Remember the diameter. The diameter of a circle is the length of the straight line that can be drawn between two points on the sphere or circle and through its center. The diameter is the longest line that can be drawn through a circle and divides the circle into two halves. The length of the diameter is also equal to the length of twice the radius. The formula for the diameter is as follows: D = 2r, where "D" stands for diameter and "r" for radius. The formula for the radius can be derived from the previous formula and is therefore: r = D / 2.
2. Divide the diameter by 2 to find the radius. If you know the diameter of a circle, all you have to do is divide it by 2 to find the radius.
   • For example, if the diameter of a circle is 4, then the street would be 4/2, or 2.

Method 2 of 3: Calculate the radius if you know the circumference

1. Think about whether you remember the formula for the circumference of a circle. The circumference of a circle is the distance around the circle. Another way to look at it is like this: the circumference is the length of the line you get when you cut the circle open at one point and lay the line straight. The formula for the circumference of a circle is O = 2πr, where "r" is the radius and π is the constant pi, which is 3.14159 ... So the formula for the radius is r = O / 2π.
   • Usually you can round pi to two decimal places (3.14), but check with your teacher first.
2. Calculate the radius with the circumference given. To calculate the radius based on the circumference, divide the circumference by 2π, or 6.28
   • For example, if the circumference is 15, then the radius is r = 15 / 2π, or 2.39.

Method 3 of 3: Calculate the radius if you know the coordinates of three points on the circle

1. Understand that three points can define a circle. Any three points on a grid define a circle that is tangent to the three points. It is the circumscribed circle of the triangle that the points form. The center of the circle can be inside or outside the triangle, depending on the position of the three points, and is at the same time the "intersection" of the triangle. It is possible to calculate the radius of the circle if you know the xy coordinates of the three points in question.
   • As an example, let's take three points defined as follows: P1 = (3,4), P2 = (6, 8), and P3 = (-1, 2).
2. Use the distance formula to calculate the lengths of the three sides of the triangle, called a, b, and c. The formula for the distance between two coordinates (x₁, y₁) and (x₂, y₂) is as follows: distance = √ ((x₂ - x₁) + (y₂ - y₁)). Now process the coordinates of the three points in this formula to find the lengths of the three sides of the triangle.
3. Calculate the length of the first side a, which runs from point P1 to P2. In our example, the coordinates of P1 (3,4) and of P2 are (6,8), so the length of side a = √ ((6 - 3) + (8 - 4)).
   • a = √ (3 + 4)
   • a = √ (9 + 16)
   • a = √25
   • a = 5
4. Repeat the process to find the length of the second side b, which runs from P2 to P3. In our example, the coordinates of P2 (6,8) and of P3 are (-1,2), so the length of side b = √ ((- 1 - 6) + (2 - 8)).
   • b = √ (-7 + -6)
   • b = √ (49 + 36)
   • b = √85
   • b = 9.23
5. Repeat the process to find the length of the third side c, which runs from P3 to P1. In our example, the coordinates of P3 (-1,2) and of P1 are (3,4), so the length of side c = √ ((3 - -1) + (4 - 2)).
   • c = √ (4 + 2)
   • c = √ (16 + 4)
   • c = √20
   • c = 4.47
6. Use these lengths in the formula for finding the radius: (abc) / (√ (a + b + c) (b + c - a) (c + a - b) (a + b - c)) .. The result is the radius of our circle!
   • The lengths of the triangle are as follows: a = 5, b = 9.23 and c = 4.47. So the formula for the radius looks like this: r = (5 * 9.23 * 4.47) / (√ (5 + 4.47 + 9.23) (4.47 + 9.23 - 5) (9.23 + 5 - 4.47) (5 + 4.47 - 9.23)).
7. First, multiply the three lengths together to find the numerator of the fraction. Then you adjust the formula.
   • (a * b * c) = (5 * 9.23 * 4.47) = 206.29
   • r = (206.29) / (√ (5 + 4.47 + 9.23) (4.47 + 9.23 - 5) (9.23 + 5 - 4.47) (5 + 4.47 - 9.23))
8. Calculate the sums between the brackets. Then place the results in the formula.
   • (a + b + c) = (5 + 4.47 + 9.23) = 18.7
   • (b + c - a) = (4.47 + 9.23 - 5) = 8.7
   • (c + a - b) = (9.23 + 5 - 4.47) = 9.76
   • (a + b - c) = (5 + 4.47 - 9.23) = 0.24
   • r = (206.29) / (√ (18.7) (8.7) (9.76) (0.24))
9. Multiply the values ​​in the denominator.
   • (18.7)(8.7)(9.76)(0.24) = 381.01
   • r = 206.29 / √381.01
10. Take the root of the product to find the denominator of the fraction.
    • √381.01 = 19.51
    • r = 206.29 / 19.52
11. Now divide the numerator by the denominator to find the radius of the circle!
    • r = 10.57