Name
LESSON
Date
Class
Reading Strategies
11-1 Focus on Vocabulary
The diagram below describes vocabulary words that are used with circles.
A secant is a line that
intersects a circle at
two points. Line 艎 is
a secant.
A tangent is a line in
the same plane as the
circle that intersects it
at exactly one point.
Line t is a tangent.
A chord is a segment
whose endpoints
_ lie
on a circle. DE is
a chord.
%
The interior of a circle is
the set of all points inside
the circle. Point X is in
the interior of the circle.
9
8
#
$
T
The point of tangency
is the point where the
tangent and the circle
intersect. Point A is a point
of tangency.
!
The exterior of a circle is
the set of all points outside
the circle. Point Y is in the
exterior of the circle.
A tangent line is perpendicular to the _
radius of a circle
drawn to the point of tangency. CA line t
A line that is perpendicular to the radius of a circle at a
point on the circle is a tangent line to the circle.
Answer the following.
of a circle is the set of all points inside the circle.
1. The
is a line that intersects a circle at two points.
2. A
3. Look at circle C above. Why is line t not a secant?
Use circle P to identify each line, segment, or point.
Z
4. secant line
2
0
K
5. point of tangency
"
6. tangent line
9
7. chord
8
8. a point in the exterior of the circle
9. a point in the interior of the circle
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All rights reserved.
10
Holt Geometry
Challenge
LESSON
11-1 Lines That Intersect Circles
Review for Mastery
LESSON
11-1 Lines That Intersect Circles continued
Theorem
Hypothesis
If two segments are tangent
to a circle from the same
external point, then the
segments are congruent.
In PQR, in which PQ 15, QR 22, and PR_
30, a
semicircle is drawn
so_
that its diameter lies on PR and it
_
QR. If S is the center of the circle,
is tangent to QP and_
find the measure of PS to the nearest hundredth.
Conclusion
F
E
C
_
EF EG
_
EF and EG are tangent to C.
Statements
In the figure above, EF 2y and EG y 8. Find EF.
2y y 8
Substitute 2y for EF and y 8 for EG.
y8
Subtract y from each side.
EF 2(8)
EF 2y ; substitute 8 for y.
16
1. All radii have equal measures.
2. mQTS mQUS 90°
2.
If a line is tangent to a circle,
then it is perpendicular to the
radius drawn to the point of
Simplify.
tangency (Theorem 11-1-1).
_
The segments in each figure are tangent to the circle.
Find each length.
5. BC
_
3. QT QU
3.
y6
M
x3
If two segments are tangent to
a circle from the same external
6. LM
B
point, then the segments are
N
congruent (Theorem 11-1-3).
A
C
2y 2
K
_
2x
D
_
4. QS QS
4.
Reflexive Property
5. QTS QUS
5.
Hypotenuse-Leg or SSS
6. UQS TQS
6.
CPCTC
PQ ___
QR
___
7.
7. Triangle Angle Bisector Theorem
L
14
6
7. RS
8. JK
J
S
P
5y
PS
2x 5
G
15 ______
22
___
30 x
x
12.16 PS
and x 19
10
7
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All rights reserved.
Holt Geometry
Problem Solving
LESSON
11-1 Lines That Intersect Circles
1. The cruising altitude of a commercial
airplane is about 9000 meters. Use the
diagram to find AB, the distance from
an airplane at cruising altitude to Earth’s
horizon. Round to the nearest kilometer.
8
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Geometry
Reading Strategies
LESSON
11-1 Focus on Vocabulary
001-072_Go08an_CRF_c11.indd 7
4/13/07 12:35:54 PM
The diagram below describes vocabulary words that are used with circles.
2. In the figure, segments that appear to be
tangent are tangent. Find QS.
A secant is a line that
intersects a circle at
two points. Line 艎 is
a secant.
3
2
2Y 9
!
1
15
4
%
5
4Y
A tangent is a line in
the same plane as the
circle that intersects it
at exactly one point.
Line t is a tangent.
A chord is a segment
whose endpoints
_ lie
on a circle. DE is
a chord.
9
"
#
The interior of a circle is
the set of all points inside
the circle. Point X is in
the interior of the circle.
27
6371
km
8
#
$
T
339 km
The point of tangency
is the point where the
tangent and the circle
intersect. Point A is a point
of tangency.
!
__› _
3. The area of H is 100, and HF 26
centimeters. What is the perimeter of
quadrilateral EFGH?
__›
4. IH, IK, and KL are tangent to A. What
is IK ?
)
%
(
Y
X
The exterior of a circle is
the set of all points outside
the circle. Point Y is in the
exterior of the circle.
+
,
(
Answer the following.
interior
1. The
68 cm
A tangent line is perpendicular to the _
radius of a circle
drawn to the point of tangency. CA line t
A line that is perpendicular to the radius of a circle at a
point on the circle is a tangent line to the circle.
X
!
Y &
*
'
47
secant
2. A
Choose the best answer.
of a circle is the set of all points inside the circle.
is a line that intersects a circle at two points.
3. Look at circle C above. Why is line t not a secant?
5. A teardrop-shaped roller coaster loop is a section of a spiral
in which the radius is constantly changing. The radius at the
bottom of the loop is much larger than the radius at the top of
the loop, as shown in the figure. Which is a true statement?
A K and M have two points of tangency.
B K, L, and M have one point of tangency.
C L is internally tangent to K and M.
D L is externally tangent to K and M.
top of loop
because it intersects the circle at only one point
Use circle P to identify each line, segment, or point.
,
+
-
Z
line z
4. secant line
2
0
bottom of loop
K
5. point of tangency
"
6. tangent line
6. G has center (2, 5) and radius 3.
H has center (2, 0). If the circles are
tangent, which line could be tangent to
both circles?
F x2
H y2
_
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All rights reserved.
J y5
9
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Geometry
XY
7. chord
7. The Hubble Space Telescope orbits
353 miles above Earth, and Earth’s radius
is about 3960 miles. Which is closest to
the distance from the telescope to Earth’s
horizon?
A 1634 mi
C 3976 mi
B 1709 mi
D 5855 mi
8
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All rights reserved.
60
point B
line k
9
G x0
.
3x 2
H
T
3y 4
RS
Let PS x. Then
K
R
Reasons
ST SU
1.
2 segs. tangent to from same ext. pt. → segs. .
EF EG
2
3
_
Draw
to the points of tangency
_radii ST
_and SU_
to PQ and QR. Draw QS.
G
_
5
0
_
_
1
4
8. a point in the exterior of the circle
point R
9. a point in the interior of the circle
point P
10
Holt Geometry
Holt Geometry