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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,

(x-h)^2 +(y-k)^2

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? 
Common Core Standard    7.G.4  7th Grade Math
Related Sites: Circumference of a Circle

Circumference of a Circle-Math Warehouse  Seven example problems in which you calculate the circumference of a circle.

Circumference of Circle Worksheets  A large choice of circumference of a circle worksheets. You have easy and hard worksheets to choose from,and each worksheet has an answer key.
Circumference of a Circle
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Circumference equals the distance around a circle

Diameter is the distance across a circle passing through the center of the circle

Radius equals the distance from the center of the circle to an edge of the circle.

Radius equals 1/2 the diameter

The Geometry ratio of pi ( written using the greek letter π)  is calculated when you take the circumference of a circle and divide by the diameter of the same circle. 

π= Circumference /Diameter 
Diameter of a circle

Definition of Circumference

Calculate the circumference of a circle with a diameter of 8 units and a radius of 4 units.

Method 1.  Circumference = pi * diameter
3.14*8=25.12 units  

Method 2. Circumference of circle = 2 * radius * p  
 2 * 4 * 3.14 = 25.12 units

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Circumference = d ● π 

Circumference = 2 ● r ● π

d= Diameter of the Circle

r = radius 

 with diameter of 8 radius of 4 circle
r =4
Diameter =8
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Circumference of a Circle Formula

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Circumference and Radius of a Circle

π=pi which is 3.14159... but this is an approximation

Circumference to Radius

The easiest method for finding radius from the circumference of a circle is to simply divide the circumference by pi, which equals the diameter. 
Next, divide the diameter by two for the radius.

For example. What is the radius of a circle with a circumference of 24 units?

Step 1. 24/π = 7.63 = diameter of the circle
Step 2. 7.63/2 = 3.81 units is the radius

What is the radius of a circle with a circumference of 314 units?

Step 1. 314/π = 99.94 = diameter of the circle.  
Step 2. 99.94/2 = 49.97 units is the radius

To find the radius from diameter simply divide the diameter by two.

Radius= Diameter/2

Radius of the circle from the area

If you know the area of a circle you can find the radius using this formula:

Radius = √Area*π

Radius from equation of the circle and 1 point.

Circumference to Diameter

If you know the circumference of a circle you can work backwards and find the diameter.
Circumference = π *diameter

Find the diameter of a circle with a circumference of 20 feet.
Let's use 3.14 for pi
20= 3.14 x
Divide each side by 3.14
20/3.14 = 3.14x/3.14
6.369 = diameter (x)

Find the diameter of a circle with a circumference of 15 feet.
15 = 3.14x
x = diameter
Divide each side by 3.14
15/3.14 = 3.14x/3.14
4.77 = diameter (x)