The circle theorems

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