Warm-Up
Exercises
Bell Work
1. What measure is needed to find the circumference
or area of a circle?
2. Find the radius of a circle with diameter 8 centimeters.
3. A right triangle has legs with lengths 5 inches and
12 inches. Find the length of the hypotenuse.
4. Solve (x + 18)2 = x2 + 242.
Warm-Up
Exercises
Notes
Definitions
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.
Warm-Up
Exercises
Notes
Definitions
A chord is a segment whose endpoints are on a circle.
A diameter is a chord that goes through the center of
the circle.
Warm-Up
Exercises
Notes
Definitions
A secant is a line that intersects a circle in two points.
A tangent is a line in the plane of the circle that
intersects the circle in exactly one point called the point
of tangency.
Warm-Up1Exercises
EXAMPLE
Tell whether the line, ray, or segment is best
described as a radius, chord, diameter, secant, or
tangent of C.
a.
AC
b.
AB
c.
DE
d.
AE
Warm-Up
Exercises
GUIDED
PRACTICE
1. In Example 1, what word best describes
AG ? CB ?
Warm-Up
Exercises
GUIDED
PRACTICE
2. In Example 1, name a tangent line and a tangent
segment.
Warm-Up2Exercises
EXAMPLE
Use the diagram to find the given lengths.
a.
Radius of
b.
c.
Diameter of A
d.
Diameter of
Radius of
A
B
B
Warm-Up
Exercises
GUIDED
PRACTICE
3. Use the diagram in Example 2 to find the radius
and diameter of C and D.
Warm-Up
Exercises
Notes
Definitions
Coplanar Circles: can intersect in three different ways
1)
2)Tangent Circles
3)Concentric Circles
Warm-Up
Exercises
Notes
Definitions
Common Tangents: a line, ray, or segment that is
tangent to two coplanar circles.
Warm-Up3Exercises
EXAMPLE
Tell how many common tangents the circles have
and draw them.
a.
b.
c.
Warm-Up
Exercises
GUIDED
PRACTICE
Tell how many common tangents the circles have and
draw them.
5.
4.
6.
Warm-Up
Exercises
Notes
Theorem 10.1
In a plane, a line is tangent to a circle iff the line is
perpendicular to a radius of the circle at its endpoint on
the circle.
Warm-Up4Exercises
EXAMPLE
In the diagram, PT is a radius of
tangent to P ?
P. Is ST
Warm-Up5Exercises
EXAMPLE
In the diagram, B is a point of tangency. Find the
radius r of C.
Warm-Up
Exercises
Notes
Theorem 10.2
Tangent segments from a common external point are
congruent.
Warm-Up6Exercises
EXAMPLE
RS is tangent to C at S and RT is tangent to
Find the value of x.
C at T.
Warm-Up
Exercises
GUIDED
PRACTICE
7.
Is DE tangent to
C?
Warm-Up
Exercises
GUIDED
PRACTICE
8.
ST is tangent to Q.Find the value of r.
Warm-Up
Exercises
GUIDED
PRACTICE
9.
Find the value(s) of x.
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
1.
Give the name that best describes the figure .
a.
CD
b.
AB
c.
FD
d.
EP
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
2.
Tell how many common tangents the circles have .
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
3.
Is AB tangent to . C? Explain.
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
4.
Find x.
Warm-Up
Exercises
For Tomorrow
Homework
HW: 10.1 (pg. 645-647) #3-10,12-13,15,18,22,24,27-28,35-36