In the diagram, a line from the centre of the circle meets a chord at its midpoint.

Find the value of .  (2 marks) 
  

In the circle centred at , the chord has length 15 and meets the chord at right angles.

Find the length of .  (1 mark) 
  

In the diagram, two chords of a circle intersect. 

Find .  (2 marks) 
  

In the diagram, two chords of a circle intersect. 

Find .  (2 marks) 
  

In the circle centred at the chord has length 7. The point lies on and has length 4. The chord passes through .

Let the length of be and the length of be .

Show that  .  (2 marks)