Circle Theorems (Cambridge (CIE) IGCSE International Maths: Core): Exam Questions

and  are points on the circumference of a circle, centre
 is a diameter of the circle.
and  are tangents to the circle.
Angle .

Work out the size of angle .

and are points on the circumference of a circle, centre
and are tangents to the circle.

By showing that at least one angle and all three sides are equal, show that triangle is congruent to triangle

and are points on a circle.
is a diameter of the circle.

Find the value of .

.............................

The points and lie on the circumference of a circle, centre.
is a tangent to the circle.

Find the value of and the value of .

The diagram shows the vertices of a triangle lying on the circumference of a circle with centre .

Find the value of .
Give a reason for your answer.

= .................... because.............................. 

The points  and  lie on the circumference of a circle, centre .
 is a tangent to the circle and angle .

Find the value of  and the value of .

 .................................    

................................ [3]

,   and   are points on the circumference of a circle with diameter .

A tangent is drawn at .

Find angle .

................................ [1] 

Find angle .

................................ [2] 

and  are points on the circumference of a circle, centre .
 is a tangent to the circle.
 is a straight line.

Angle 

Work out the size of the angle marked .

and  are points on the circumference of a circle, centre .
and  are tangents to the circle.

Angle 
Angle 
Angle 

i) Explain why reflex angle .

[3]

ii) Work out the size of angle .

[2]

and are points on the circle, centre . is a tangent to the circle at .

i) Write down the mathematical name for the line .

[1]

ii) Explain why angle is 90°.

[1]

iii) Find the value of .

= ................................................. [3]

The diagram shows a circle, centre , with diameter .
and lie on the circumference of the circle.

i) Find the value of .
Give a reason for your answer.

  = ..................... because ...........................

[3]

ii) Find the value of .
Give a reason for your answer.

  = ..................... because ....................................

[2]

iii)Draw a tangent to the circle at .

[1]

The diagram shows a circle, centre with diameter .
Angle = 63°.

i) Find angle .

Angle = ................................................... [2]

ii) = 12 cm

Calculate .

= ............................................. cm [2]

K, L and M are points on the circle.
KS is a tangent to the circle at K.
KM is a diameter and triangle KLM is isosceles.  

Find the value of .  

................................................ [2]

The diagram shows a circle, centre , with points and on the circumference.
The line touches the circle at . is parallel to and angle .

i) Write down the mathematical name of the line .

................................................. [1]

ii) Write down the reason why angle is .

......................................................................................................................................................     

...................................................................................................................................................... [1]

iii) Find angle.

................................................ [1]

iv) Write down the reason why angle = angle .

...................................................................................................................................................... [1]

v) Complete the statement using a mathematical word.

Triangle is ................................................................. to triangle . [1]

.

Calculate

via) ,

......................................... cm [2]

vib) ,

......................................... cm [2]

via) the area of triangle .

.........................................cm² [2]