Circle: Area and Circumference

Circle Components

• A circle is a closed arc around a center point, with a constant distance between the center and any point on the edge, known as the radius.
• The diameter is the distance of a line segment that runs from one edge of the circle to the opposite edge, through the center point.
• Other components of a circle include an arc (a portion of the circle's edge), a chord (a line segment connecting two points on the circle's edge), and a segment (a section of the inside of the circle).

Circle Angles and Lines

• A circle angle is formed by two radii with vertices at different locations on the circle's edge.
• A tangent is a line that touches the circle at only one point, outside of the circle.
• A secant is an extension of a chord, a line that runs through the circle and intersects two points on the circle's edge.

Measuring a Circle

• The area and circumference of a circle can be measured using various units (imperial or metric), but the units used must be units of length.
• Common imperial units of length include inches, feet, and yards, while common metric units include millimeters, centimeters, and meters.

Calculating the Area of a Circle

• The area of a circle is the region or space measured inside the circle, or the total number of square units inside the circle.
• The area of a circle can be calculated using the formula: A = πr^2, where π is approximately 3.14 and r is the radius.
• The area of a semi-circle is half of the area of a circle.
• The area of a circle can also be found using the diameter: A = π(d/2)^2.

Calculating the Circumference of a Circle

• There are two ways to find the circumference of a circle: using the diameter or the radius.
• The circumference of a circle using the diameter is: C = πd.
• The circumference of a circle using the radius is: C = 2πr.
• Examples of finding the circumference of a circle include calculating the amount of siding needed for a circular pool or finding the circumference of a decorative circular plate.

Finding the Area Using Circumference

• To calculate the area of a circle using circumference, one must know the area and circumference formulas.
• The area of a circle can be found using the circumference by: A = (C^2) / (4π).
• This involves dividing the circumference by π, squaring the result, and multiplying by π.