Circle Theorems (Cambridge (CIE) IGCSE Maths: Core)

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 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]