### Exercise 1

##### Question 1

Diagram
**NOT** accurately drawn

In the diagram, *A*, *B*, *C *and *D *are points on the circumference of a circle, centre *O*. Angle *BAD *= 70°. Angle *BOD *= *x*°. Angle *BCD *= *y*°.

(a) Work out the value of *x*. Give a reason for your answer.

(b) Work out the value of *y.* Give a reason for your answer.

##### Question 2

*P*, *Q*, *R* and *S* are points on the circumference of a circle, centre *O*. *PR* is a diameter of the circle. Angle *PSQ* = 56°.

(a) Find the size of angle *PQR*. Give a reason for your answer.

(b) Find the size of angle *PRQ*. Give a reason for your answer.

(c) Find the size of angle *POQ*. Give a reason for your answer.

##### Question 3

The diagram shows a circle, centre *O*. *AC* is a diameter. Angle *BAC* = 35°.*D* is the point on *AC* such that angle *BDA* is a right angle.

(a) Work out the size of angle *BCA*. Give reasons for your answer.

(b) Calculate the size of angle *DBC*.

(c) Calculate the size of angle *BOA*.

##### Question 4

*A, B, C *and *D *are points on the circumference of a circle, centre *O. BOD *is a straight line. Angle *COD = *70°

(a)
Find the size of angle *BAD. *Give a reason for your answer.

(b) Find the size of angle *CBD. *Give a reason for your answer.

##### Question 5

*A*, *B*, *C* and *D* are points on the circumference of a circle, centre *O*. *AC* is a diameter of the circle. Angle *DAC* = 20º.

(a) Find the size of angle *ACD*.

(b) Find the size of angle *DBC*. Give a reason for your answer.

##### Question 6

Diagram **NOT **accurately drawn

*A, B, C* and *D* are points on the circle, centre *O*. Angle *BOD* = 86º

(a) Work out the size of angle *BAD.* Give a reason for your answer.

(b) Work out the size of angle *BCD.*

##### Question 7

*A ,B, C* and *D* are points on a circle, centre *O*. Angle *BOD* = 116°

(a) Calculate the size of angle *BAD*.

Given that *BC* = *CD*.

(b) Calculate the size of angle *DBC*.

##### Question 8

*A*, *B*, *C* and *D* are four points on the circumference of a circle. *ABE* and *DCE* are straight lines. Angle *BAC* = 25°. Angle *EBC* = 60°.

(a) Find the size of angle *ADC*.

(b) Find the size of angle *ADB*

Angle *CAD* = 65°. Ben says that *BD* is a diameter of the circle.

(c) Is Ben correct? You must explain your answer.

**Answer Keys | Go to ****Exercise 2**** | Go back to ****Circle Theorems**