The radius of a circle is the distance from the center of the circle to any point on its circumference. It is a fundamental measurement in geometry and is used in various mathematical calculations involving circles.

**Definition:**The radius of a circle is a line segment from the center of the circle to any point on its circumference.**Symbol:**The radius is commonly denoted by the letter "r".**Measurement:**The length of the radius can be measured in units such as centimeters, inches, or meters.**Relationship with Diameter:**The radius is half the length of the diameter of a circle.

There are several important formulas involving the radius of a circle:

**Calculate Circumference:**The circumference of a circle can be calculated using the formula:

C = 2πr**Calculate Area:**The area of a circle can be calculated using the formula:

A = πr^{2}

Here are some practice problems to test your understanding of the radius:

- Find the radius of a circle with a circumference of 12π.
- If the radius of a circle is 5 cm, calculate its area.
- What is the diameter of a circle with a radius of 8 inches?

Remember, the key to mastering the concept of radius is to practice using it in various calculations and problems involving circles.

Now that you have a solid understanding of the radius of a circle, you can confidently apply this knowledge to solve geometry problems and understand the properties of circular shapes.

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Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes.

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to solve problems in other areas of mathematics, such as number and measurement.