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.
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.
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).
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.
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).
The video above will explain more in detail about the Geometry of Circles,
with the help of several examples.
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