### Exercise 2

##### Question 1

Diagram ** NOT** accurately drawn

The diagram shows a circle, centre *O.A, S, B *and

*T*are points on the circumference of the circle.

*PT *and *PS *are tangents to the circle*.AB *is parallel to

*TP.*

Angle *SPT *= 44°.

Work out the size of angle *SOB.*

##### Question 2

*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.

##### Question 3

*T*, *A* and
*B* are points on the circumference of the circle, centre *O*.*AT*
is a diameter of the circle.

Angle *BTC* = 40°

Angle *TAB*
= 30°

Explain why *TC* cannot be a tangent to the circle.

##### Question 4

Diagram **NOT **accurately drawn

The diagram shows a circle centre *O*.*A*, *B *and *C *are points on the circumference.

*DCO *is a straight line.*DA *is a tangent to the circle.

Angle *ADO = *36°

(a) Work out the size of angle *AOD*.

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

##### Question 5

In the diagram, *A*, *B* and *C* are points on the circumference of a circle, centre *O*. *PA* and *PB* are tangents to the circle.

Angle *ACB* = 75°.

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

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

**Answer Keys | Go to Exercise 1 | Go back to ****Circle Theorems**