impossible GCSE circle theorem question

ps. please excuse the terrible diagram ....

it should say:

PAQ is a tangent to the circle at A
BC = CD
angle BAQ = 32 degrees

find the size of angle BAD

anyone?
Saf!

ps. please excuse the terrible diagram ....

it should say:

PAQ is a tangent to the circle at A
BC = CD
angle BAQ = 32 degrees

find the size of angle BAD

do you know what the answer is.....i got 64 degrees, but i could easily be wrong, since i've forgotten all these circle theoroms
I get 116 degrees. Is that right?
Allternate segment theorem to get <ADB and <ABD , and because it's an isoceles, 2x + y = 180
2 times 32 - 64 180 -64
i did tht paper in exam conditions in class and i got 64 degrees which was wrong but i dont know the right answer! anybody know the right answer??
xxx
hey PPl

I just tried that Q and a mate of mine did aswell. We both got BAD = 64
Are you sure thats wrong ? Could your teacher of marked it badly ?

Chris
this is how i did it...
angle BDA = 32 , because of angle in opposite segment rule
angle DBC = 32 , because of alternate ('Z') angles
angle BDC = 32 , because triangle BCD is isoceles
angle BCD = 116 , because angles in a triangle add up to 180
therefore angle BAD = 64 , because opposite angles in a cyclic quad. add up to 180.