Question

In a circle AD is a diameter of a circle with center O . If AB is parallel to CD ,probe that AB=CD.

Answer 1

See diagram.

Look at the two triangles ABD and ACD. 
As AB is parallel to CD and AD intersects the two lines AB and CD, the angles marked as x and y are same in two triangles.

angle BAD = angle CDA
angle BDA = angle CAD

hence angle B = angle C.

Now, the two triangles are similar.   there is a common side AD for two triangles. Hence all the sides are same. 

Hence AB = CD.