Name: ________________________________________
Unit 9 Review
(10.2) If the vertex of an angle is the center of the circle, then the measure of the intercepted arc is equal to
the measure of the central angle.
Use the figure to the right to find the indicated arc measures below.
1. KL = 100
2. LM = 60
3. KM = 200
4. KN = 80
(10.4) If the vertex of an angle is on the circle, then the measure of the intercepted arc is ____________ of the
measure of the inscribed angle.
Find the value of each variable below.
xo
5.
6.
7.
c = 28
x = 80
x = 63
(10.5) If the vertex of an angle is inside the circle, then the measure of the angle is half of the SUM of the
intercepted arcs.
Find the value of each variable below.
xo
8.
9.
10.
x = 106
x = 133
x = 70
(10.5) If the vertex of an angle is outside the circle, then the measure of the angle is half of the DIFFERENCE of
the intercepted arcs.
Find the value of each variable below.
xo
11.
12.
13.
x = 70
x = 16
x = 84
(10.1) If two tangent segments share a common endpoint, then they are congruent to each other.
Find the value of each variable below. All lines that appear to be tangent are.
14.
15.
16.
x=5
x=4
c=2
(10.6) If two chords intersect inside a circle, then the product of the parts of one chord is equal to the product
of the parts of the other chord.
Find the value of each variable below.
17.
18.
19.
x=7
x=4
x=5
(10.6) If two secant lines intersect outside a circle, then the product of the EXTERNAL segment and the ENTIRE
secant segment of one is equal to the product of the EXTERNAL segment and the ENTIRE secant segment of
the other.
Find the value of each variable below.
20.
21.
22.
x=5
x=9
(10.6) If a secant line intersects a tangent line outside a circle, then the product of the EXTERNAL segment and
the ENTIRE secant segment is equal to the square of the tangent segment.
Find the value of each variable below.
23.
24.
25.
x=7
x = 15
x = 12
(10.1) A tangent line to a circle is perpendicular to the radius at their point of intersection.
Find the value of each variable below.
26.
27.
28.
x = 64
x = 33
x = 117
(10.3) In the same circle, if two chords are congruent, then their intercepted arcs are also congruent
If one chord is a perpendicular bisector of another chord, then the first chord is a diameter
In the same circle, two chords are congruent if and only if they are equidistant from the center.
Find the measure of AB
29.
30.
31.
AB = 61
AB = 65
AB = 91
(10.4) If a quadrilateral is inscribed inside a circle, then the opposite angles of the quadrilateral will be
supplementary.
If a triangle is inscribed inside a circle and one of the sides of the triangle is a diameter of the circle, then the
triangle is a right triangle and the diameter is its hypotenuse.
32.
33.
34.
q = 100; r = 20
x = 72; y = 90
m = 120; k = 60
(10.1) The measure of any minor arc is less than 180o.
The measure of any semicircle is equal to 180o.
The measure of any major arc is more than 180o.
A minor arc is named with only two points, while a major arc is named with three points.
Arc Length and Extra Practice
Find the indicated measure for the circle shown. Remember to use a proportion to solve.
35.
36.
37.
32.0 cm
109.7 in
74.3o
38.
39.
40.
50.0o
35.5
8.6
41.
42.
43.
4.2 m
29.3 cm
3.14 ft
Find the length of AB
Find the value of each variable below.
(3x - 75)o
44.
45.
46.
x = 75
x = 150
x = 43