Question

prove that the line joining the mid point of two parallel chords of a circle passes through the centre.

Answer 1

Recall one important thing when you are solving this question:
The perpendicular bisector of any chord passes through the center of the circle.

So when you construct the diagram, remember to mark the right angles (∠OAZ and ∠OBX in the diagram). 

Also, you need to identify what you are supposed to prove (joining mid point passes through the center). So you need to prove that AOB is a straight line.
To do that, we can construct another line OC//WX//YZ.

The proof

∠BOC = ∠OAZ = 90° (corresponding angles, OC//YZ)
∠COA = ∠XBO = 90° (corresponding angles, OC//WX)
∠AOB 
= ∠BOC + ∠COA
=180°

So AOB is a straight line. Therefore AB passes through O.

Answer 2

Step-by-step explanation:

I hope this diagram will help you