Angle Properties of Circles

The diagram shows a circle, centre O.

What is the value of x

• 106

• 53

• 37

• 90

The diagram shows a circle, centre O.

What is the value of z.

• 116

• 244

• 58

• 122

The diagram shows a circle, centre O.
Points A, B, C and D lie on the circumference.
AB=BC
What is the value of angle ADC

• 76

• 52

• 104

• 38

The diagram shows a circle, centre O.
P, Q, R and S are points on the circumference.
Select all the correct statements.

• Angle QPS = Angle QRS = 90, because right angle in a semicircle

• Angle SQP=27, because tangent is perpendicular to the radius

• Angle PSQ=63, because angle in alternate segment

• Angle SPQ=27, because angles in the same segment

The diagram shows a circle, centre O.

What is the value of w.

• 104

• 73

• 21

• 42

The diagram shows circle with AB as a diameter.

Angle BAC and ACB are in the ration 5:7.

What is the value of BAC.

• 75

• 37.5

• 52.5

• 90

A, B, C, D, and E lie on a circle, centre O.

What are the values of p and q?

• p=30, q=18

• p=18, q=30

• p=36, q=15

• p=20, q=30

AD is a diameter of the circle ABCDE.

AB and ED are parallel lines.

What are the values of w, x, y and z?

• w=30, x=22, y=30, z=52

• w=30, x=30, y=22, z=52

• w=52, x=22, y=30, z=30

• w=22, x=30, y=22, z=52

P, Q, R and S lie on a circle centre O.

TP and TQ are tangents to the circle.

What are the values of w, x and y?

• w=26, x=128, y=52

• w=32, x=64, y= 26

• w=26, x=116, y=54

• w=26, x=128, y=62

A,B, C, and D lie on a circle, centre O.

SCT is a tangent and is parallel to OB.

What are the values of x, y, z and the reflex angle AOC.

• x=40, y=20, z=120, reflex angle AOC=130

• x=40, y=25, z=115, reflex angle AOC=230

• x=40, y=25, z=115, reflex angle AOC=130

• x=40, y=25, z=130, reflex angle AOC=230