A circle is a closed curve in which all points on the curve are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle passing through the center is called the diameter. The ratio of the circumference of a circle to its diameter is a constant value denoted by the Greek letter π (pi), which is approximately 3.14159. The formula for the circumference of a circle is C = 2πr, where r is the radius, and the formula for the area of a circle is A = πr^{2}.

**Radius:**The distance from the center of a circle to any point on the circle.**Diameter:**The distance across a circle passing through the center, equal to 2 times the radius.**Circumference:**The distance around the edge of a circle, given by the formula C = 2πr or C = πd, where d is the diameter.**Area:**The measure of the space enclosed by a circle, given by the formula A = πr^{2}.

**Circumference:** C = 2πr or C = πd (where r is the radius and d is the diameter)

**Area:** A = πr^{2} (where r is the radius)

- Find the circumference of a circle with a radius of 5 cm.
- Find the area of a circle with a diameter of 12 inches.

**Solution:** C = 2π(5) = 10π cm, or approximately 31.42 cm.

**Solution:** r = d/2 = 12/2 = 6 inches, A = π(6^{2}) = 36π square inches, or approximately 113.10 square inches.

In summary, a circle is a closed curve with all points equidistant from the center. The radius is the distance from the center to any point on the circle, the diameter is the distance across the circle passing through the center, the circumference is the distance around the edge of the circle, and the area is the measure of the space enclosed by the circle. Key formulas for circles include C = 2πr and A = πr^{2} for the circumference and area, respectively.

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Data Analysis and Probability (NCTM)

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.

Select and use appropriate statistical methods to analyze data.

Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.