topic 12 review - birdville schools...14. 15. c 16. a8 b8 d8 c 8 40 8 a 8 c 8 b 8 20 8 < 8 a 8 b...
TRANSCRIPT
TOPIC VOCABULARY
chord, p. 492
p. 499
p. 486
p. 505
p. 486
Check Your Understanding
Use the figure to choose the correct term to complete each sentence.
1. <
EF>
is (a secant of, tangent to) }X .
2. DF is a (chord, secant) of }X .
3. △ABC is made of (chords in, tangents to) }X .
4. ∠DEF is an (intercepted arc, inscribed angle) of }X .
C
D
A
EX
BF
Topic 12 Review
12-1 Tangent Lines
ExercisesUse }O for Exercises 5–7.
5. What is the perimeter of △ABC?
6. OB = 128. What is the radius?
7. What is the value of x?
A
O
C
B
3
5
2
x 8
608
ExamplePA
>
and PB>
are tangents. Find x.
The radii are perpendicular to the
tangents. Add the angle measures
of the quadrilateral:
x + 90 + 90 + 40 = 360
x + 220 = 360
x = 140
B
P
A
x 8O 408
Quick ReviewA tangent to a circle is a line that intersects the circle at
exactly one point. The radius to that point is perpendicular
to the tangent. From any point outside a circle, you can
draw two segments tangent to a circle. Those segments are
congruent.
511PearsonTEXAS.com
12-3 Inscribed Angles
ExercisesFind the value of each variable. Line O is a tangent.
13. 14.
15. 16.
a8
b8
d8
c 8
408
a 8
c 8
b 8
208
<
c 8a 8
b 8
d 8
728
598
b 8
a 8
d 8 c 8
458
<
1408
ExampleWhat is mPS
¬? What is mjR?
m∠Q = 60 is half m PS¬
, so
m PS¬
= 120. ∠R intercepts the
same arc as ∠Q, so m∠R = 60.
P
Q R
S
608
Quick ReviewAn inscribed angle has its
vertex on a circle, and its sides
are chords. An intercepted arc
has its endpoints on the sides
of an inscribed angle, and its
other points in the interior of the
angle. The measure of an inscribed
angle is half the measure of its
intercepted arc.
AInterceptedarc
Inscribed angle
B C
12-2 Chords and Arcs
ExercisesUse the figure at the right for Exercises 8–10.
8. If AB is a diameter and CE = ED,
then m∠AEC = ? .
9. If AB is a diameter and is at right
angles to CD, what is the ratio of
CD to DE?
10. If CE =12 CD and m∠DEB = 90,
what is true of AB?
Use the circle below for Exercises 11 and 12.
11. What is the value of x?
12. What is the value of y?
A
B
EC D
x
y
95
5
ExampleWhat is the value of d?
Since the chord is bisected, m∠ACB = 90.
The radius is 13 units. So an auxiliary
segment from A to B is 13 units. Use the
Pythagorean Theorem.
d2 + 122 = 132
d2 = 25
d = 5
d
CA
B
13
12
12
Quick ReviewA chord is a segment whose endpoints
are on a circle. Congruent chords are
equidistant from the center. A diameter
that bisects a chord that is not a
diameter is perpendicular to the chord.
The perpendicular bisector of a chord
contains the center of the circle.
512 Topic 12 Review
12-4 Angle Measures and Segment Lengths
ExercisesFind the value of each variable.
17.
18.
19.
20.
x 8
1008
268
a 8 b 8
1458
458
5
10
6
x
10
8
5
x
ExampleWhat is the value of x?
(x + 10)10 = (19 + 9)9
10x + 100 = 252
x = 15.2
9
10
19
x
Quick ReviewA secant is a line that intersects a circle at two points.
The following relationships are true:
a ? b 5 c ? d
1
x 8O
d
c
b
ay 8
m/1 5 (x 1 y)12
(w 1 x)w 5 ( y 1 z)y
Bb 8w
x
zy
a8
O
m/B 5 (a 2 b)12
( y 1 z)y 5 t 2
B
t
zy
b 8
a 8
O
m/B 5 (a 2 b)12
513PearsonTEXAS.com