Deck 7: Circles

Question 1

In , and are minor arcs for which m m . Which must be true?

A)
B)m m
C) is nearer to center O than
D)None of These

Answer 1

D

Question 2

In the circle shown, m = (m   m ).

Answer 2

False

Question 3

In the circle, m = 68 ° and m = 74 ° . Find m .

A)34 °
B)37 °
C)71 °
D)142 °

Answer 3

C

Question 4

In , m = 103 ° and m = 77 ° . Which statement is false?

A) is a semicircle
B) would be a diameter
C) is a minor arc
D) would be a right angle

Question 5

Where m = x and and are tangents to the circle, m .

Question 6

If m = 105 ° and m = 73 ° , find the measure of (not shown).

Question 7

From an external point E , tangents and are drawn to . If m = 78 ° , find the measure of minor arc .

Question 8

If m = 105 ° and m = 27 ° , find m .

A)39 °
B)44 °
C)78 °
D)88 °

Question 9

In a circle in which m   m , it follows that .

Question 10

In the figure, secants and intersect the circle at points R and S respectively. If m = 36 ° and m : m = 4:1, find m .

Question 11

For a circle, and are tangents from an external point D . How are and related?

Question 12

is tangent to at point B . If m = 53 ° , find m .

Question 13

In the circle, chords and intersect at point P . If m = 63 ° and m = 75 ° , find m .

Question 14

If central angle intercepts minor arc of , then m = m .

Question 15

In , m = 60 ° and BC = 12. Find AB .

A)3
B)
C)6
D)

Question 16

If m = 75 ° in , then m = 275 °.

Question 17

In a circle (or congruent circles)containing two unequal chords, the shorter chord is nearer the center of the circle.

Question 18

Because intercepts of , m = m .

Question 19

With and both tangent to the circle as shown, find an expression that represents the measure of both and .

Question 20

In the figure, and are tangents to the circle from point D . If m = 84 ° , find m .

A)42 °
B)84 °
C)96 °
D)None of These

Question 21

If is circumscribed about the circle in such a way that m = 90 ° and m = 110 ° , which is true?

A) cannot be a right angle
B)m m
C)m = 200 °
D)

Question 22

If m = 37 ° , find m .

Question 23

In the circle shown, m = m . Are these arcs congruent?

Question 24

In , m = 138 ° . Find m .

A)64 °
B)69 °
C)138 °
D)None of These

Question 25

Find the measure of the angle formed by the hands of a clock at exactly 4:10 PM.

Question 26

With chords and intersecting in the interior of the circle, what expression can be used to find m ?

Question 27

Let point E lie in the exterior of . How many tangent lines can be constructed to  from point E ?

Question 28

For cyclic quadrilateral ABCD , m and m . Determine the value of x .

A)x = 50
B)x = 100
C)x = 120
D)x = 130

Question 29

To determine the measure of , which expression should be calculated. (m   m )or (m   m )?

Question 30

In this order, points R , S , T , U , and V are equally spaced on a circle in such a way                 . What type of figure is formed by the chords , , , , and ?

Question 31

In , m = 58 ° . Find m .

Question 32

An angle inscribed in a semicircle is an obtuse angle.

Question 33

In the circle, m = 102 ° and m = 76 ° . Where M is the midpoint of , find m .

Question 34

When two secants intersect at a point in the exterior of a circle, the measure of the angle formed is one-half the positive difference of the measures of the two intercepted arcs.

Question 35

What is the measure of the angle formed by the hands of a clock at exactly 4:20 PM?

A)30 °
B)33 °
C)35 °
D)10 °

Question 36

If two inscribed angles of a circle intercept the same arc, these angles are congruent.

Question 37

With the circle inscribed in , it follows that AR = AS , BS = BT , and CR = CT .

Question 38

For , the length of radius is 10 cm. For parallel chords and , AB = 12 cm and CD = 16 cm. How far apart are the parallel chords?

Question 39

If points A and B are the endpoints of a diameter and C is any other point on , find the measure .

A)75 °
B)85 °
C)95 °
D)None of These

Question 40

In , m   m .

Question 41

A line through the center of a circle perpendicular to a chord (not a diameter)bisects the chord.

Question 42

In the figure, is tangent to the circle at point T while is a secant for the circle.

Question 43

In , radius   chord at point C . If OD = 5 and AB = 8, find OC .

A)3
B)3.5
C)
D)4

Question 44

For the circle shown, chords and intersect at point X . With RX = 6, XS = 8, TX = x + 8 and XV = x , find the length of .

Question 45

Point P lies in the exterior of so that is tangent to the circle. Also, is a secant that intersects at B and C , where P - B - C . If PB = 9 and BC = 7, find PA .

A)10
B)12
C)16
D)None of These

Question 46

is a tangent while is a secant for the circle shown. If TR = 6 and RS = 3, find RV .

Question 47

For a given circle, tangent is drawn from external point E so that point T is the point of tangency. Where E - R - S , secant intersects that circle at points R and S . Find an expression that is equivalent to .

Question 48

Externally tangent circles P and Q touch at point T and have the line of centers . How does one construct the common internal tangent for circles P and Q ?

Question 49

The length of radius of the circle shown is 10 inches. If CD = 12 inches and AB = 16 inches, how much closer to the center is chord than ?

A)2 inches
B)4 inches
C)6 inches
D)14 inches

Question 50

In the figure, chords and intersect at point X . If RX = 8, TX = 12, and XS = 9, find XV .

A)5.6
B)6
C)7.5
D)None of These

Question 51

Two circles that are internally tangent have three common tangent lines.

Question 52

has been constructed tangent to at point T and to at point W . How are radii and related?

A)congruent
B)congruent and parallel
C)parallel
D)None of These

Question 53

has a radius length of 5 while has a radius length of 7. If OT = 12, find the number of common tangents for the two circles.

Question 54

In , chord   diameter . With chords and , quadrilateral RSTV is formed. Being as specific as possible, what type of quadrilateral is RSTV ?

Question 55

In , radius   chord at point C . If OR = 5 and CR = 2, find AB .

Question 56

is circumscribed about the circle. If DF = 14, FG = 16, and DG = 12, find DM .

Question 57

Diameter of is perpendicular to chord at point E . If CD = 18 and OE = 5, find the length of .

Question 58

In a circle, chords and intersect at point X . If m = 98 ° , m = 54 ° , and m = 72 ° , which chord among , , , and would be longest?

Question 59

Congruent circles have the same length of radius while concentric circles have the same center.

Question 60

is tangent to at point B . If OB = 4 and AB = 3, find AC .

A)1
B)1.2
C)1.5
D)2

Question 61

is inscribed in P in such a way that m m m . Which angle of has the greatest measure?

Question 62

In , one side of is diameter while a second side is chord . If AC = PB = 5, find the length of chord .

Question 63

is tangent to at point B . If the length of radius of is r , AC = 1, and AB = 3, write an equation that involves r .

Question 64

In the figure, is said to be circumscribed about the circle.

Question 65

For the concentric circles shown, is tangent to the inner circle and a chord of the outer circle. If the radius of the inside circle is 5 and of the outer circle is 13, find AB .

A)8
B)12
C)16
D)24

Question 66

Square MNPQ is circumscribed about . If the radius of measures 8 cm, find the length of a diagonal of square MNPQ .

Question 67

How many common tangents do two internally tangent circles have?

Question 68

To construct the tangent to at point T on the circle, we construct a line perpendicular to at point T .

Question 69

Chords , , and of are parallel and . Which chord lies nearest the center point P ?

Question 70

Quadrilateral ABCD is inscribed in . If m = 49 ° , find m .

Question 71

is circumscribed about in such a way that . Which angle of has the greatest measure?

Question 72

The circles shown have 4 common tangents, two of which are internal and two of which are external.

Question 73

In the figure, suppose that auxiliary line segments and are drawn. What method allows you to conclude that ?

Question 74

When a quadrilateral is circumscribed about a circle, how are the sides of the quadrilateral related to the circle?

Question 75

When a quadrilateral is inscribed in a circle, each pair of opposite angles is complementary.

Question 76

How many common tangents do these circles have?

A)1
B)2
C)3
D)4

Question 77

For (not shown), tangent touches the circle at point of tangency T . How are radius and tangent related?

Question 78

The vertices of quadrilateral ABCD lie on . It is correct to say that:

A)Quadrilateral ABCD is inscribed in
B)Quadrilateral ABCD is circumscribed about
C) is inscribed in quadrilateral ABCD
D)None of These