Circles Arcs and Angles- tangent lengths
Name:
Date:
1.
In the accompanying diagram, the measure of
arc AB is 48. What is the measure of inscribed
angle ACB ?
2.
What is the measure of an inscribed angle that
intercepts an arc whose measure is 200?
A.
3.
4.
100
B.
200
C.
300
5.
In the accompanying gure, the measure of minor
arc AB is 100. Find the measure of inscribed
angle ACB.
6.
In the accompanying diagram, PA and PB are
tangent to circle O. If mOPBA = 70, nd mOP.
7.
Two tangents to a circle from an external point
intercept a major arc of 300 . Find the number of
degrees in the angle formed by the two tangents.
8.
In the accompanying diagram, AB is a diameter
of circle O and chord CD intersects diameter AB
at E. If mAD = 100 and mAC = 40, nd mODEB.
D. 50
In the accompanying gure, the measure of
angle AOB is 50. Find the measure of inscribed
angle ACB.
(
In the accompanying diagram, mBC = 120. Find
the measure of inscribed angle BAC.
page 1
9.
In the accompanying diagram, chords AB and CD
intersect in the circle at E. If mBC = 60 and
mAD = 80, nd mOAEC.
15.
In the accompanying diagram, tangent PA and
secant PBC are drawn to circle O from point P.
If mAC = 80 and mAB = 60, what is the measure
of OP ?
10.
A.
10
B.
20
C.
60
D. 70
(
!
In the accompanying diagram, BD is tangent to
circle O at B, BC is a chord, and BOA is a
diameter. If mAC : mCB = 1 : 4, nd mODBC.
(
Tangents PA and PB are drawn from point P to
the same circle. The major arc intercepted by
the tangents is three times the minor arc. Find
mOAPB
(
14.
In the accompanying diagram, isosceles
triangle ABC is inscribed in the circle. If AB = CB
and mAB = 150, nd mOB.
17.
In the accompanying gure of circle O, the
measure of AC is 84 . What is the measure of
OABC ?
(
16.
12.
In the diagram below, chords AB and CD intersect
at E. If mOAEC = 4x, mAC = 120, and mDB = 2x,
what is the value of x ?
13.
(
!
!
If PA and PB are tangents to circle O and the
ratio of major arc AB to minor arc AB is 2 : 1,
what is mOP ?
(
11.
A.
12
B.
20
A.
21
B.
C.
30
D. 60
C.
84
D. 168
42
In the accompanying diagram, PBA and PCD
are secants to the circle. If mOP = 40 and
mAD = 120, nd mBC.
page 2
Circles Arcs and Angles- tangent lengths
18.
(
!
In the accompanying diagram, PA is tangent
to circle O at A and PBC is a secant. If
AB : BC : CA = 2 : 3 : 4, nd mOP.
23.
In the accompanying diagram, PAB and PCD are
externally tangent to circles O and O0 . If PB = 16
and CD = 10, nd PA.
24.
In the accompanying diagram of circle F, FN
bisects HJ and mNJ = 68. Find mHG.
25.
!
In the accompanying diagram, BA is tangent to
circle O at A. Radii OA and OC are drawn, and
!
OC is extended to intersect BA at B. If BA = 15
and OB = 17, nd the measure of a radius of
circle O.
In the accompanying diagram of circle O, chord
AB is parallel to chord CD. If mAC = 100, nd
mOBOD.
(
19.
22.
(
(
!
In the accompanying diagram, DCFG is tangent
!
to circle O at F, ECH is a secant intersecting the
circle at A and B, mAB = 140 and mAF = 160. If
FC = 10, nd AF to the nearest tenth.
(
20.
In a circle, an inscribed angle intercepts an arc of
140 . Find the number of degrees in the measure
of the angle.
21.
!
In the accompanying diagram, AB is tangent to
circle O at B and ACD is a secant. If mOA = 40
and mBD = 140, nd mBC.
page 3
Circles Arcs and Angles- tangent lengths
26.
29.
In the accompanying diagram, AFB, AEC, and
BGC are tangent to circle O at F, E, and G,
respectively. If AB = 32, AE = 20, and EC = 24,
nd BC.
In the accompanying diagram of circle O, diameter
AB is perpendicular to chord CD and intersects
CD at E, AE = 9, and EB = 4.
What is ED?
27.
28.
A.
In the accompanying diagram, segments RS, ST,
and TR are tangent to circle O at A, B, and C,
respectively. If SB = 3, BT = 5, and TR = 13, what
is the measure of RS ?
30.
In the accompanying diagram of circle O,
diameter AB is perpendicular to chord CD at E,
CD = 8, and EB = 2. What is the length of the
diameter of circle O ?
8
B.
7
C.
6
D. 4
The accompanying diagram represents circular
pond O with docks located at points A and B.
From a cabin located at C, two sightings are taken
!
that determine an angle of 30 for tangents CA
!
and CB.
What is mOCAB?
A.
page 4
30
B.
60
C.
75
D. 150
Circles Arcs and Angles- tangent lengths