Section 9.1


Objectives:

  • Define a circle and its associated parts, and use them in constructions.
  • Define and use the degree measure of arcs.
  • Define and use the length measure of arcs.
  • Prove a theorem about chords and their intercepted arcs.


Definitions:

  • Circle: a circle is a closed plane curve consisting of all points
at a given distance from a point within it called the center.
  • Radius: a straight line extending from the center of a circle or
sphere to the circumference or surface:
(the radius of a circle is half the diameter.)
  • Chord: a segment in which its endpoints line up on the circle.
  • Diameter: a diameter is a cord which it includes the center point
of the circle.
  • Arc: a part of the circle were it isn`t broken.
  • Endpoints: any points that had divided into two parts.
  • Semicircle: it is an arc which the endpoints are the
endpoints of the diameter. (it is also known as the
half circle)
  • Minor arc: It is an arc that is shorter then the semicircle.
  • Major arc: It is the arc that is longer then the semicircle.
  • Central angle: it is an angle in the plane whose vertex
is in the center of the circle.
  • Intercepted arc: When the endpoints of an arc are on the sides
of the central angle and the other points are inside the angle.

click here to see the equation of a circle




Arc Length:

L=M/360°{2(3.14)r}
-or-
L=M/360°(2external image pie%20copy.jpgr)

Degree measure of arcs:

The central angle is the measure of a minor arc. The degree measure of a
major arc is 360 degrees minus the degree measure of it's minor arc.
The degree measure of a semicircle is 180 degrees, half of 360.

Finding the length of an arc:

r is radius of the circle and M is the degree measure of an arc of the
circle, the length,L, of the arc is given by the following:
L= M/360 degrees(2Pi r)