Warm-Up Exercises
1. What measure is needed to find the circumference
or area of a circle?
ANSWER
radius or diameter
2. Find the radius of a circle with diameter 8 centimeters.
ANSWER
4 cm
Warm-Up Exercises
3. A right triangle has legs with lengths 5 inches and
12 inches. Find the length of the hypotenuse.
ANSWER
13 in.
4. Solve 6x + 15 = 33.
ANSWER
3
Warm-Up Exercises
5. Solve (x + 18)2 = x2 + 242.
ANSWER
7
Warm-Up1Exercises
EXAMPLE
Identify special segments and lines
Tell whether the line, ray, or segment is best
described as a radius, chord, diameter, secant, or
tangent of C.
a.
AC
SOLUTION
a.
AC is a radius because C is the center and A is a
point on the circle.
Warm-Up1Exercises
EXAMPLE
Identify special segments and lines
Tell whether the line, ray, or segment is best
described as a radius, chord, diameter, secant, or
tangent of C.
b.
AB
SOLUTION
b.
AB is a diameter because it is a chord that
contains the center C.
Warm-Up1Exercises
EXAMPLE
Identify special segments and lines
Tell whether the line, ray, or segment is best
described as a radius, chord, diameter, secant, or
tangent of C.
c.
DE
SOLUTION
c.
DE is a tangent ray because it is contained in a
line that intersects the circle at only one
point.
Warm-Up1Exercises
EXAMPLE
Identify special segments and lines
Tell whether the line, ray, or segment is best
described as a radius, chord, diameter, secant, or
tangent of C.
d.
AE
SOLUTION
d.
AE is a secant because it is a line that
intersects the circle in two points.
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 1
1. In Example 1, what word best describes
AG ? CB ?
SOLUTION
AG Is a chord because it is a segment whose
endpoints are on the circle.
CB is a radius because C is the center and B is a point
on the circle.
Warm-Up
Exercises
GUIDED
PRACTICE
2.
for Example 1
In Example 1, name a tangent and a tangent segment.
SOLUTION
A tangent is DE
A tangent segment is DB
Warm-Up2Exercises
EXAMPLE
Find lengths in circles in a coordinate plane
Use the diagram to find the given lengths.
a.
Radius of
b.
c.
Diameter of A
d.
Diameter of
Radius of
A
B
B
SOLUTION
a.
The radius of
A is 3 units.
b.
The diameter of A is 6 units.
c.
The radius of
d.
The diameter of B is 4 units.
B is 2 units.
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 2
3. Use the diagram in Example 2 to find the radius
and diameter of C and D.
SOLUTION
a.
The radius of
C is 3 units.
b.
The diameter of C is 6 units.
c.
The radius of D is 2 units.
d.
The diameter of D is 4 units.
Warm-Up3Exercises
EXAMPLE
Draw common tangents
Tell how many common tangents the circles have
and draw them.
a.
c.
b.
SOLUTION
a.
4 common tangents
b.
3 common tangents
Warm-Up3Exercises
EXAMPLE
Draw common tangents
Tell how many common tangents the circles have
and draw them.
c.
SOLUTION
c.
2 common tangents
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 3
Tell how many common tangents the circles have and
draw them.
4.
SOLUTION
2 common tangents
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 3
Tell how many common tangents the circles have and
draw them.
5.
SOLUTION
1 common tangent
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 3
Tell how many common tangents the circles have and
draw them.
6.
SOLUTION
No common tangents
Warm-Up4Exercises
EXAMPLE
Verify a tangent to a circle
In the diagram, PT is a radius of
tangent to P ?
P. Is ST
SOLUTION
Use the Converse of the Pythagorean Theorem.
Because 122 + 352 = 372,
PST is a right triangle and
ST PT . So, ST is perpendicular to a radius of P
at its endpoint on P. By Theorem 10.1, ST is tangent
to P.
Warm-Up5Exercises
EXAMPLE
Find the radius of a circle
In the diagram, B is a point of tangency. Find the
radius r of C.
SOLUTION
You know from Theorem 10.1 that AB BC , so
ABC
is a right triangle. You can use the Pythagorean
Theorem.
AC2 = BC2 + AB2 Pythagorean Theorem
(r + 50)2 = r2 + 802
r2 + 100r + 2500 = r2 + 6400
100r = 3900
r = 39 ft .
Substitute.
Multiply.
Subtract from each side.
Divide each side by 100.
Warm-Up6Exercises
EXAMPLE
Find the radius of a circle
RS is tangent to C at S and RT is tangent to
Find the value of x.
C at T.
SOLUTION
RS = RT
Tangent segments from the same point are
28 = 3x + 4
Substitute.
8=x
Solve for x.
Warm-Up
Exercises
GUIDED
PRACTICE
7.
Is DE tangent to
ANSWER
Yes
for Examples 4, 5 and 6
C?
Warm-Up
Exercises
GUIDED
PRACTICE
8.
for Examples 4, 5 and 6
ST is tangent to Q.Find the value of r.
ANSWER
r=7
Warm-Up
Exercises
GUIDED
PRACTICE
9.
for Examples 4, 5 and 6
Find the value(s) of x.
ANSWER
+3 = x
Daily
Homework
Quiz
Warm-Up
Exercises
1.
Give the name that best describes the figure .
a.
CD
ANSWER
c.
b.
secant
ANSWER
ANSWER
d.
FD
chord
AB
tangent
EP
ANSWER
radius
Daily
Homework
Quiz
Warm-Up
Exercises
2.
Tell how many common tangents the circles have .
ANSWER
One tangent; it is a vertical line through the point of
tangency.
Daily
Homework
Quiz
Warm-Up
Exercises
3.
Is AB tangent to . C? Explain.
ANSWER
2
2
2
Yes; 16 + 30 = 1156 = 34 so AB AC, and a line
radius at its endpoint is tangent to the circle.
to a
Daily
Homework
Quiz
Warm-Up
Exercises
4.
Find x.
ANSWER
12