Going Around in Circles

1
Going Around in Circles!

• Chapter 10 Honors Geometry

2
Parts of a Circle and their Definitions

• Circle
• Set of all points in a plane that are a given
  distance from a given point in the plane.

CenterThe given point referred to in the
definition of the circle. A circle is named by
its center!
CENTER
Given point
Given distance
RADIUS
RadiusThe given distance referred to in the
circle definition the segment connecting the
center to the circle the distance from the
center to the circle.
3
Parts of a Circle and their Definitions
Concentric Circles
Two or more coplanar circles with the same center
4
Parts of a Circle and their Definitions
A point is inside (in the interior) a circle if
its distance from the center is less than the
radius.
A point is on a circle if the distance from the
center is equal to the radius.
A point is outside (in the exterior) a circle if
its distance from the center is more than the
radius.
POINT on a circle
INTERIOR of a circle
EXTERIOR of a circle
5
Parts of a Circle and their Definitions
Chord
A chord of a circle is a segment that connects
any two points on the circle.
A chord that passes through the center is called
the DIAMETER of the circle
6
Parts of a Circle and their Definitions
Circumference
The perimeter of or distance around a circle is
called the circumference of a circle.
Check out about how the circumference of the
earth was found http//video.google.com/videoplay?
docid8157409168878797983qcircumferencehlen
7
Parts of a Circle and their Definitions
Area of a Circle
8
Parts of a Circle and their Definitions
Enjoy the video!
Circles Radius Diameter Pi from Math Upgrade
9
Theorems for Circle Radii and Chords

• If a radius is perpendicular to a chord then it
  bisects the chord
• If a radius of a circle bisects a chord that is
  not a diameter, then it is perpendicular to that
  chord.
• The perpendicular bisector of a chord passes
  through the center of the circle.

10
Circles!

• Lets try some problems!

11
Theorems for Circle Congruent Chords

• If two chords of a circle are equidistant from
  the center, then they are congruent.
• If two chords of a circle are congruent, then
  they are equidistant from the center of the
  circle.