Circle Terminology and Properties

Study Notes

A circle is defined as the collection of all points in a plane equidistant from a central point, known as the center.
The center point serves as the focal point for the circular shape.
The diameter of a circle is a special type of chord that passes directly through the center, dividing the circle into two equal halves.
A radius is the distance from the center to any point along the circle's edge, with all radii being equal in length.
Circumference refers to the total distance around the circle, equivalent to the perimeter of a circular shape.
A chord is defined as a line segment whose endpoints lie on the circumference of the circle.

Pi (π) is approximately 3.14159 and represents the ratio of the circumference of a circle to its diameter, fundamental in circle calculations.
According to the Tangent to a Circle Theorem, a line that is tangent to the circle forms a right angle with the radius at the point of tangency.
A secant intersects a circle at two distinct points, indicating the line extends through the circle's area.

A semi-circle is simply half of a full circle, measured as 180 degrees.
The central angle of a circle is formed by two radii, with the vertex located at the circle's center.
The intercepted arc connected to a central angle is significant, as the measure of the angle is half that of the arc.
A major arc spans an angle greater than 180 degrees, while a minor arc measures less than 180 degrees.

A sector of a circle is the area enclosed by two radii and their corresponding arc, resembling a slice of pizza.
The length of an arc can be calculated using the relationship: Central Angle/360 = Arc Length/Circumference.
The area of a circle quantifies the total space enclosed within its boundary, necessary for various applications in geometry.

The standard form equation for a circle is represented as (x-h)² + (y-k)² = r², where (h, k) indicates the center coordinates, and r signifies the radius.