Welcome Back!
Today we will be doing new seating
charts, reviewing your current grades,
then taking notes on Chapter 10.1.
Warm- Up
4/14/15
Directions: Multiply the following binomials
1. (x + 1)2 = ?
Hint: (x + 1)2 = (x+1)(x+1)
2. (x − 5)2 = ?
3.
Warm- Up
4/14/15
Directions: Multiply the following binomials
1. (x + 1)2 = ?
x2 + 2x + 1
Hint: (x + 1)2 = (x+1)(x+1)
2. (x − 5)2 = ?
3.
x2 − 10x + 25
r=5
10.1 Use
Properties of
Tangents
Use properties of a
tangent to a circle
Vocabulary:
• A circle is the set of all
points in a plane that are
equidistant from a given
point called the center of
the circle.
• A segment whose
endpoints are the center
and any point on the circle
is a radius.
• A chord is a line segment
that intersects a circle in
two points.
• The diameter of a circle is
a chord that goes through
the center of the circle.
Vocabulary
• A secant is a line that
intersects a circle in
two points.
• A tangent is a line in
the plane of a circle
that intersects the
circle in exactly one
point, the point of
tangency.
Example 1:
• Tell whether the line or segment is best
described as a radius, chord, diameter,
secant, or tangent of circle C.
a) DC
b) BD
c) DE
d) AE
Example 2
Coplanar Circles
• Two circles can intersect in 2 points, 1 point, or 0
points.
• Coplanar Circles that intersect in one point are
called tangent circles.
• Coplanar circles that have a common center are
called concentric
Common Tangents
• A line, ray, or segment that is tangent to
two coplanar circles is called a common
tangent.
Example 3: Draw common
Tangents
• Tell how many
common tangents
the circles have.
Theorem 10.1
• In a plane, a line is
tangent to a circle
if and only if the
line is
perpendicular to a
radius of the circle
at its endpoint on
the circle.
Example 4:
• In the diagram, AB
is a radius of circle
A. Is BC tangent
to circle A.
Explain.
Example 5:
• In the diagram, S
is a point of
tangency. Find the
radius of r of circle
T.
Theorem 10.2:
• Tangent segments from a common
external point are congruent
Example 6: Use properties
of tangents.
• In circle C, DA, is tangent at A and DB is
tangent at B. Find x.
 Homework 
4/13:
WORKBOOK
Pg 184 #1-4, #12-17
4/14: Pg 184 #5-11, 18, 21-22