Circle Theorems/Properties

The tangents to a circle from the same point will be

• equal length

• parallel

• perpendicular

• different lengths

The angles in the same segment from a common chord are:

• equal

• 30 degrees

• add up to 90 degrees

The opposite angles in a cyclic quadrilateral

• are equal

• add up to 180 degrees

• add up to 360 degrees

• are 90 degrees

The points E, F and G lie on the circumference of a circle, centre O.

JGH is a tangent to the circle.

Find the value of x and the value of y.

• x=32 , y= 58

• x=29, y=58

• x=32 , y=32

DAE is a tangent to a circle. Write down the size of angle ABC. Give the reason for your answer

• 61 , alternate segments

• 61 , same segments

• 63, alternate segments

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

What are the values of p and q?

• p=30, q=18

• p=18, q=30

• p=36, q=15

• p=20, q=30