Lesson 21: Circles

In the figure below, G is the center of the circle, LK is a diameter, H lies on the circle, J lies outside the circle on LK, and JM is tangent to the circle at M. Which of the following angles or minor arcs has the greatest degree measure?

• LM

• MK

• JMG

• ZLHK

• JML

Tags

CCSS.HSG.C.A.2

Points A and B lie on the circle below, where central angle ∠ACB measures 110°. What is the measure of ∠ABC?

• 35°

• 45°

• 55°

• 110°

• Cannot be determined from the given information

Tags

CCSS.HSG.C.A.2

In the circle shown below, chords TR and QS intersect at P, which is the center of the circle, and the measure of ∠PTS is 30°. What is the degree measure of minor arc RS?

• 30°

• 45°

• 60°

• 90°

• Cannot be determined from the given information

Tags

CCSS.HSG.C.B.5

In the figure above, lines m and r are tangent to the circle at points P and Q, respectively, and C is the center of the circle. If ∠r = 130°, what is y?

• 25°

• 50°

• 65°

• 75°

• 90°

Tags

CCSS.HSG.C.A.2

Four points, A, B, C, and D, lie on a circle having a circumference of 17 units. B is 5 units counterclockwise from A. C is 3 units clockwise from A. D is 11 units clockwise from A and 6 units counterclockwise from A. What is the order of the points, starting with A and going clockwise around the circle?

• A, B, C, D

• A, D, B, C

• A, C, D, B

• A, C, B, D

• A, D, C, B

Tags

CCSS.HSG.C.B.5

The ratio of the radii of two circles is 4:9. What is the ratio of their circumferences?

• 2:3

• 4:9

• 16:81

• 4:81

• 9:18

Tags

CCSS.7.G.A.1

Points M and N are the endpoints of the diameter of a circle with center O, as shown below. Point P is on the circle, and angle MOP measures 60°. The shortest distance along the circle from M to P is what percent of the distance along the circle from M to N?

• 60%

• 50%

• 33 1/3%

• 16 2/3%

Tags

CCSS.HSG.C.B.5

A circle with radius 10 cm is divided into 3 congruent arcs. What is the length, in centimeters, of each of the 3 arcs?

Tags

CCSS.HSG.C.B.5

As shown in the figure below, a clock has a minute hand that measures 5 cm from its tip to the center of the clock. To the nearest centimeter, what is the distance traveled by the tip of the minute hand between 2:10 p.m. and 5:30 p.m.?

• 31

• 81

• 108

• 105

• 173

Tags

CCSS.HSG.C.B.5

Which of the following is closest to the tank's volume, in cubic feet?

• 310

• 630

• 1,300

• 2,500

• 5,000

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3