Properties of Circles Tangent

In the diagram, PQ and QR are tangents to a circle at P and R respectively. Which of the following statements is correct?

The diagram shows a circle with centre O. Find the value of y.

• 111

• 69

• 55.5

• 21

In the diagram, RTS is a tangent to a circle at point T and the arc length of minor sector OQP is 1/5 of the circumference of the circle with centre O. Find the value of x.

• 75

• 72

• 36

• 18

Identify the straight lines that are tangents to the circle in the diagram. You can choose more than one answer.

• AB

• RS

• KJ

• LM

• TU

What is the value of x?

• 22

• 25

• 15

• 20

State the angles of equal size in the diagram. You can choose more than one answer.

In the diagram, RST is a straight line. Find the value of x + y.

• 150

• 160

• 170

• 210

In the diagram, KLMN is a tangent to a circle MTR. RSM is a straight line. Find the value x.

• 50

• 70

• 110

• 120

In the diagram, ABC is a straight line. Choose the correct statement below. You can choose more than one answer.

In the diagram, LMN is a tangent of the circle at point M. Choose the correct statements below. You can choose more than one answer.