i need help with proving the 1st part.thx
HI
Since BC is parallel to AD , it is clear that $\displaystyle \angle CBD=\angle BDA$ and
$\displaystyle \angle BCA=\angle CAD $
Now use the properties of circles , where angles in the same segment are equal , so
$\displaystyle \angle BCA=\angle BDA$ and $\displaystyle \angle CBD=\angle CAD$ .
and you should be able to make your deduction now .