Angles and line segments

This task is about using geometric properties to explain why line segments are the same length.
The centre of this circle is marked with a dot.
circle and line segment diagram
[Not drawn to scale]  

Question 2Change answer

a)  The line segments OA and OB are the same length.
     Explain why.
     

Question 2Change answer

b)  i)  What is the size of the shaded angle marked 'z'?  degrees
 
      ii) The line segments DB and AB are the same length.
          Explain why.