1. Intro to Circles
Geometry 1B

2. Things we already know…
Circles
The set of all points in a plane that are a given distance (radius) from a given point (center)in the plane
Radius
Segment that joins the center to a point on the circle
All radii of a circle are congruent
Diameter
A segment that has endpoints on the circle and passes through the center of the circle.
Area of a circle
Circumference of a circle
Diameter

3. Are the circles the same?
All circles have the same shape.
Their sizes are determined by the radius.
If two circles have congruent radii, then the two circles are congruent.
If two circles have the same center, then the circles are concentric circles.

4. Where is the point?
A point is in the interior of a circle if its distance from the center is less than the radius.
d < r
A point is in the exterior of a circle if its distance from the center is greater than the radius.
d > r
A point is on a circle if its distance
from the center is equal to the radius.
d = r

5. a b a : b a to b Ratio: A comparison of two quantities using division.
Three ways to write it… a b
a : b
a to b

6. Proportion:
A comparison of two equal ratios. a b c d =

7. Cross-Multiplication:
cross-mul·ti·ply (krôsmlt-pl, krs-) intr.v. cross- mul·ti·plied, cross-mul·ti·ply·ing, cross- mul·ti·plies
To multiply the numerator of one of a pair of fractions by the denominator of the other.
4 x 4 = 16 2 4 4 8 =
2 x 8 = 16

8. So if…
a b c d =
Then…
a x d = b x c

9. Rules of equality…
Please explore the following presentation and write the notes in your binder. online.com/objects/ViewObject.aspx?ID=GEM220 4

10. Central Angle and Arc Length
A central angle is an angle whose vertex is the center of a circle, and whose sides pass through a pair of points on the circle.
Part of the circumference of a circle.

11. Chords
A chord of a circle is a segment joining any two points on a circle.
What is the longest chord of a circle?
A diameter of a circle is a chord that passes through the center of the circle.

12. Chord Relationships
Please refer to Chord Notes in your binder to explore 4 different cases.