In this lesson, we will learn how to find the circumference of a circle, arc length, area of a circle, area of sector, tangent of a circle, inscribed and crcumscribed polygons.

Any line segment joining two points on the circle is called a chord. The terms “radius” and “diameter” can also refer to line segments: A radius is any line segment joining a point on the circle and the center of the circle, and a diameter is any chord that passes through the center of the circle.

The distance around a circle is called the circumference of the circle, which is analogous to the perimeter of a polygon. The ratio of the circumference C to the diameter d is the same for all circles and is denoted by the Greek letter π (pi).

This video will help you understand the relationship between the radius diameter and circumference of a circle.

C = πd = 2πr

In this video, you will learn about Central Angles and their relationship to Arcs. You will also learn about Chords and their relationships to Arcs and Central Angles.

This video lesson discusses how to find the length of an arc. First, the arc length theorem is reviewed and explained. An example of find the length of a major arc is modeled. The given information is the measure of the related minor arc and the radius of the circle.

This video shows how to get the area of a circle and how it relates to radius and diameter.

This video shows how to find the area of a sector.

A tangent to a circle is a line that intersects the circle at exactly one point, called the point of tangency. If a line is tangent to a circle, then a radius drawn to the point of tangency is perpendicular to the tangent line. The converse is also true; that is, if a line is perpendicular to a radius at its endpoint on the circle, then the line is a tangent to the circle at that endpoint.

This video provides example problems of determining unknown values using the properties of a tangent line to a circle.

A polygon is inscribed in a circle if all its vertices lie on the circle, or equivalently, the circle is circumscribed about the polygon. If one side of an inscribed triangle is a diameter of the circle then the triangle is a right triangle. Conversely, if an inscribed triangle is a right triangle, then one of its sides is a diameter of the circle.

A polygon is circumscribed about a circle if each side of the polygon is tangent to the circle, or equivalently, the circle is inscribed in the polygon.

This video shows how to solve problems involving quadrilaterals inscribed in circles.

This video shows that if an inscribed triangle is a right triangle, then the hypotenuse is the diameter. If an inscribed angle has a diameter as one of its sides, then its a right triangle.

Tjis video gives a lesson on polygons inscribed in and circumscribed about a circle.

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