Finding an Angle Between Two Tangents to a Circle

In the diagram, PTR and QTS are straight lines. Find the value of x.

• 28

• 32

• 36

• 48

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

• 25

• 30

• 35

• 40

The diagram shows a semicircle with centre O. Find the value of x.

• 35

• 40

• 45

• 50

The diagram shows a circle with centre O. The minor arc PQ and the minor arc RS are of equal length. Find the value of x.

• 20

• 25

• 30

• 35

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

• 150

• 160

• 170

• 210

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 semicircle with centre O. Find the value of x.

• 22

• 28

• 34

• 68

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

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

• 50

• 70

• 110

• 120