**Helpful Links**

There are few different circle theorems that can be used to answer this question. Therefore, here is a link to the whole circle theorem section.

**Mark Scheme**

**Working**

*A*,

*B*,

*C*and

*D*are points on the circumference of a circle, centre

*O*.

*FDE*is a tangent to the circle.

a) Show that

*y*–

*x*= 90

You must give a reason for each stage of your working.

Dylan was asked to give some possible values for

*x*and

*y*.

He said,

“

*y*could be 200 and

*x*could be 110, because 200 – 110 = 90”

b) Is Dylan correct?

You must give a reason for your answer

*See mark scheme for answers!***Question**

13)

*A*,

*B*,

*C*and

*D*are points on the circumference of a circle, centre

*O*.

*FDE*is a tangent to the circle.

a) Show that

*y*–

*x*= 90

You must give a reason for each stage of your working.

**[3 marks]**

Dylan was asked to give some possible values for

*x*and

*y*.

He said,

“

*y*could be 200 and

*x*could be 110, because 200 – 110 = 90”

b) Is Dylan correct?

You must give a reason for your answer

**[1 mark]**