Circles in Geometry

A series of free, online High School Geometry Video Lessons.
Videos, worksheets, and activities to help Geometry students.

In this lesson, we will learn

• the locus and definition of a circle and a sphere
• about central angles and intercepted arcs
• chords and the center of a circle

Locus and Definition of a Circle and Sphere

A locus is a set of points that meet a given condition. The definition of a circle locus of points a given distance from a given point in a 2-dimensional plane. The given distance is the radius and the given point is the center of the circle. In 3-dimensions (space), we would define a sphere as the set of points in space a given distance from a given point.
How to define a circle and a sphere using the word locus.
This video describes the locus theorem.

Central Angles and Intercepted Arcs

A central angle is an angle whose vertex is on the center of the circle and whose endpoints are on the circle. The endpoints on the circle are also the endpoints for the angle’s intercepted arc. The angle measure of the central angle is congruent to the measure of the intercepted arc which is an important fact when finding missing arcs or central angles.
How to define a central angle and find the measure of its intercepted arc; how to describe the intercepted arcs of congruent chords.
This geometry video math lesson deals with circle geometry. It focuses on how to identify congruent central angles, chords, and arcs when given either a central angle, a chord, or an arc.

Chords and a Circle’s Center

A chord is a line segment whose endpoints are on a circle. If a chord passes through the center of the circle, it is called a diameter. Two important facts about a circle chord are that (1) the perpendicular bisector of any chord passes through the center of a circle and (2) congruent chords are the same distance (equidistant) from the center of the circle.
How to define a chord; how to describe the effect of a perpendicular bisector of a chord and the distance from the center of the circle.
This geometry video math lesson deals with circle geometry. The main focus of this video is using the Chords Equidistant from the Center of a Circle Theorem. The theorem states: chords equidistant from the center of a circle are congruent and congruent chords are equidistant from the center of a circle.

Chords of circles. Chords, perpendicular bisectors and diameters.

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