Circle Theorems

ANGLES AND ARC MEASURES

100

Find the measure of arc BC

140 degrees

200

Find the measure of arc DF

129 degrees

300

Find arc CFD 

306 degrees

400

Find the measure of arc AD

48 degrees

500

Find angle SPQ 

146 degrees

CIRCUMFERENCE AND AREA

100

Find the circumference of a circle with a diameter of 12 inches.

37.68 in

200

Find the area of a circle with a diameter of 13 cm.

132.67 square cm 

300

Find the area of a circle with a circumference of 6 ft

2.87 square ft

400

The circumference of a coin is about 76 mm. What is the area?

459.87 square mm

500

Find the circumference of the circle with an area of 69.08 square feet.

29.46 ft

ARC LENGTH AND SECTOR AREA

100

Find the area of the sector

11.8 m²

200

A person standing on the earth notices that a 747 Jumbo Jet flying overhead subtends an angle of 0.45°. If the length of the jet is 230 feet, find its altitude to the nearest thousand feet. 

29,000 feet

300

A lawn sprinkler located at the corner of a yard is set to rotate through 90° and project water out 30.0 feet. What area of the lawn is watered by the sprinkler?

 

707 ft²

400

Find the area of the segment

2.57 in²

500

The minute hand of a clock is 6 in. long. How far does the tip of the hand travel in 35 minutes? (*assume the minute hand touches the edge of the clock)

21.98 inches

WHAT'S THE ANGLE?

100

Find angle CDE

76 degrees

200

Given that angle ABC is 27 degrees and angle BAC is 30 degrees, find the measure of angle BAD

123 degrees

300

Find the sum of the measures ACB and DAE

75 degrees

400

Find the missing angles n, p, m

n = 41 degrees

p = 61 degrees

m = 29 degrees

500

Find angles x, y, z

x = 40 degrees

y = 25 degrees

z = 115 degrees

TANGENT AND SECANTS

100

Find the measure of angle V

114 degrees

200

Find the measure of the arc AD and CB

AD = 80 degrees

CB = 30 degrees

300

Find x

x = 40 degrees

400

Find the measure of angle DFE and DGB

angle DFE = 67 degrees

angle DGB = 88 degrees

500

The radius of circle 𝑨 is 𝟒. 𝑫𝑪̅ and 𝑪𝑬̅ are tangent to the circle with 𝑫𝑪 = 𝟏𝟐. Find the measure of angle C, the arc 𝑫𝑬, and the area of quadrilateral 𝑫𝑨𝑬𝑪 rounded to the nearest hundredth.

 

Angle C = 36.87 degrees

Measure DE = 143.13 degrees

The area of DAEC = 48 square units