Hi, here are 3 sums which I need help in proving.

1) PQ is a tangent to the circle at A and O is the center of the circle. If BC is parallel to PQ, prove that angle BOA = 2x angle CAQ.

2) AC is a tangent at A to the circle, center O. BC is perpendicular to CA. Prove that BC is parallel to OA and AB bisects angle OBC.

3) The chords AB and CD intersect at E and the tangent PA is parallel to chord CD. Prove that AB bisects angle CBD.

Thanks for your explanations.