geometry b - unit 4: circles: arc and angle relationships

given that m<acb = 52, what is the arc length of aqb?

77π/15 in.

if m<p = (6x + 6), what is the value of x?

8

what is the length of arc ef?

9.75

to prove that the circles are similar, reina must perform a rigid transformation, followed by a similarity transformation. which transformations map circle b onto circle a?

translate 6 units right, then dilate about its new center by a scale factor of 4/3

if m<qzr = (2x + 9) and m<pzo = (4x - 11), what is the value of x?

x = 10

if rs = 4x + 8 and tv = 8x - 23, what is the value of x?

x = 7.75

lesson 18

circumference and arc length

lesson 15

similarity and arc measures in circles

if you were to forget the formula for the area of a circle, what's something you can do to calculate it?

use a parallelogram that has a base of 1/2 the circumference and a height of the radius.

what is m<efj?

60

which two transformations will map circle p onto circle q? select all that apply.

0.25 of 1 reflect in the y-axis dilate with a scale factor of 2

which statement correctly defines the radian measure for angle bad?

1/r

if xpz = 271, and xyz = (4x + 15), then x =

19

if the central angle measures 123, and the radius of the roundabout is 50 meters, how many meters must Jamie sprint to reach shelly?

107

if m<cot = 146 and ct = 35.7 units, what is the measure of ot?

14 units

if mij = 46, what is the measure of angle hok?

167

if m<lmj = (6x - 70), what is the value of x?

29

what length of rope (radius) will he need to accomplish this activity?

30 ft

if m<mcn = 147 and the length of mn = 392pi/15 inches, what is the length of cn?

32 inches

what is the m<bed?

34

if m<opr = 70, what is m<oqr?

35

if m<mno = 82, what is m<olm?

98

lesson 16

angles, arcs, and chords

lesson 19

areas in circles

if circle a is translated so that its center is at point b, which transformation should be performed next to show that the circles are similar?

dilate the translated circle so that it is the same size as circle b.

omar is told that ∠emf ≅∠gmh, ef = 2x − 3, and gh = 10x − 43. he is asked to find the length of gh. what is the length of gh?

gh = 7

lesson 17

inscribed angles and quadrilaterals

what steps should lita take to correctly solve this problem?

lita knows that m∠qcr = 74 and that the whole circle has a measure of 360, so the portion of the area she wants to find is 74/360∘. therefore, she must multiply 74/360∘ times the area, which is πr2.

what is the measure of major arc jlk?

206

what is the measure of the central angle that defines major arc mpn?

270

if m<vbc = (3x + 4), what is the value of x?

28.7

if m<aob = 71, what is the measure of arc ab?

71

what is the arc length of bg?

π feet

what is m<lke?

35

what is the area of the sector enclosed by central angle qcr?

37π/180

if the measure of ad = 78, what is m<aqd?

39

if vw = (23x + 4), what is the value of x?

4.3

what is the length of arc fe?

4.42

if m<vwa = 120 and m<bwc = (32x - 27), what is the value of x?

4.6

if the circle has a diameter of 8 ft, what is the area of the shaded sector?

512π/45

what is m<eqd, in degrees?

52

if m<h = 115, what is m<j?

65

if m<pqr = (12x - 2) and pr = (20x - 10), what is m<pqr?

70

if ca denotes the circumference of ⨀a and cb denotes the circumference of ⨀b, which equation is true?

d1 *cb = d2 * ca

examine the diagram, where d1 refers to the diameter of ⨀a and d2 refers to the diameter of ⨀b. keeping in mind that all circles are similar, which proportion is accurate?

d1/d2 = circumference ⨀a / circumference ⨀b

if m<efg = (3x + 11) and m<gce = (5x - 23), what are the measures of the central and circumscribed angles?

m<efg = 83, m<gce = 97

what is the measure of m<p and m<n?

m<p = 96, m<n = 84

if circle a is dilated so that it is the same size as circle b, which transformations could be performed next to show that the circles are similar? select all that apply.

rotate the dilated circle 180 about point c translate the dilated circle so that its center is at point b reflect the dilated circle over a horizontal line through point c

which statement correctly defines a radian measure?

the radian measure is the ratio of a circle's arc length to its radius.