Geometry: Getting Started - Circles
This is a free lesson from our course in Geometry
 
   
This lesson explains the concepts of Geometry of the Circles and relationship amongst different parts of the Circle, You’ll learn beginning with the review of concepts of the earlier learnt terms. The contents will be explained by the instructor in own handwriting and using video, with the help of several examples.
Circle A circle is the set of all points in a plane that are equidistant from a fixed point of the plane called the center of the circle. If the center of a circle is point O, the circle is called circle O.
Radius A radius (r) of a circle (plural, radii) is a line segment from the center of the circle to any point of the circle (Fig: 1). The distance across a circle through the center is called the diameter, which equals to 2r.
Circle-All radii of the same circle are Congruent
(More text below video...)
<h2> Geometry - Getting Started - Circles</h2> <p> center, geometry, circle, radius, diameter, chord, video, point, distance, line segment, geometry help, solution, example, practice questions, quizzes</p> <p> A circle is the set of points that are equidistant from a special point in the plane. The radius is a line segment joining the center of the circle with a point on the circle. </p>
Other useful lessons:
Measuring Circles
Equation of a circle in standard form
Circles- arcs, chords, tangents, sector, segment, secant
Inscribed and Circumscribed Polygons
(Continued from above)
For example: look at a pizza pie to understand diameter and radius. The pizza shown below has been sliced into eight equal parts through its center. A radius is formed by making a straight cut from the center to a point on the circle. A straight cut made from a point on the circle, passing through its center to another point on the circle, is an example of diameter. Notice that, a circle has many different radii and diameters, each passing through its center.  Diameter and Radius
Remember it: Theorem, “All radii of the same circle are congruent” (Fig: 2).
Now you’ll explore further about the relationship of a circle and plane. A circle divides the plane into three parts:
• points inside the circle
• points outside the circle
• points on the circle
Interior of a circle
The interior of a circle is the set of all points whose distance from the center of the circle is less than the length of the radius of the circle (Fig: 3).
Interior, Exterior and Central Angles of a Circle
Exterior of a circle
The exterior of a circle is the set of all points whose distance from the center of the circle is greater than the length of the radius of the circle (Fig: 4).
Central Angles
A central angle of a circle is an angle whose vertex is the center of the circle. In the (Fig: 5), LOM and MOR are central angles.
Chord
A chord of a circle is a line segment whose endpoints are points of the circle. In the (Fig: 6), chords of circle O.
Chord of a Circle
Diameter
A diameter of a circle is a chord that has the center of the circle as one of its points. In the (Fig: 7 above), AOC is the diameter. If the length of the radius of circle O is r, and the length of the diameter is d, then- d = OA + OC = 2r
A circle may have many chords. Some chords pass through the center and others do not. As seen above, chord that passes through the center is the diameter. Thus clearly diameter of a circle is the longest chord of that circle. Note that a diameter satisfies the definition of a chord; however, a chord is not necessarily diameter (Fig: 8 & 9 below).
Diameter of a Circle is a Chord but Reverse is not always true
The video above will explain more in detail about the Geometry of Circles, with the help of several examples.
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