Tangent to a Circle Theorem

Find the value of the angle marked x....

• 102

• 51

• 129

• 78

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

In the diagram, TP and TQ are tangents to a circle with centre O. Find each value of x

• 80

• 45

• 90

• 180

extension

diagram shows a tangent to a circle with centre O. Find x and y in each case

• x = 12°

  y = 156°

• x = 100°

  y = 50°

• x = 62°

  y = 28

• x = 30°

  y = 60°

Find the value of the angle marked x....

• 50

• 100

• 80

• 90

Find the value of the angle marked x....

• 76

• 38

• 152

• 14

In the diagram, TP and TQ are tangents to a circle with centre O. Find each value of x

• 5x

• 90

• 15

• 180

Find the value of the angle marked x....

• 90

• 45

• 50

• 100

Assume that lines that appear to be tangent are tangent. O is the center of the circle. What is the value of x?

• 90

• 309

• 129

• 39