1) 90°

Reason: the angle between a tangent and a radius is 90°

2) 58°

3)

a) 70°

Reason: tangents that meet at the same point are equal in length; therefore, AC and BC are equal. This means that ABC is an isosceles triangle, which results in angles CAB and CBA being the same. Also, angles in a triangle add up to 180°.

b) 90°

Reason: the angle between a tangent and a radius is 90°

c) 20°

d) 140°

4) 20°

Reason: the angle between a tangent and a radius is 90°

2) 58°

3)

a) 70°

Reason: tangents that meet at the same point are equal in length; therefore, AC and BC are equal. This means that ABC is an isosceles triangle, which results in angles CAB and CBA being the same. Also, angles in a triangle add up to 180°.

b) 90°

Reason: the angle between a tangent and a radius is 90°

c) 20°

d) 140°

4) 20°

**Working**

**Questions**

You may use a calculator for the following questions. All of the diagram in the questions are not drawn to scale.

1) The line is a tangent to the circle at point A.

What is the size of angle

2) The line is a tangent to the circle at point C.

*x*? Give a reason for your answer.2) The line is a tangent to the circle at point C.

What is the size of angle

3) There are two tangents on the outside of the circle below. One of the tangents touches the circle at point A and the other tangent touches the circle at point B. The two tangents meet each other at point C.

*y*?3) There are two tangents on the outside of the circle below. One of the tangents touches the circle at point A and the other tangent touches the circle at point B. The two tangents meet each other at point C.

a) What is the size of angle CAB? Give reasons for your answer.

b) What is the size of angle 0BC? Give a reason for your answer.

c) What is the size of angle 0AB?

d) What is the size of angle A0B?

4) There are two tangents on the outside of the circle below. One of the tangents touches the circle at point A and the other tangent touches the circle at point B. The two tangents meet each other at point C.

b) What is the size of angle 0BC? Give a reason for your answer.

c) What is the size of angle 0AB?

d) What is the size of angle A0B?

4) There are two tangents on the outside of the circle below. One of the tangents touches the circle at point A and the other tangent touches the circle at point B. The two tangents meet each other at point C.

What is

*x*?