Math Is Fun Forum

I need help with two-column proofs.

The first problem is this picture:

Given:PA and PB are tangents to circle O
Prove:OP bisects angle APB

I have to figure out the blanks this two-column proof:
Statements:
1) PA and PB are tangents to Circle O
2)OP is congruent to OP
3)OA is congruent to OB
4)OA is perpendicular to PA;OB is perpendicular to PB
5)Angle OAP and Angle OBP are right angles
6) Triangle OAP is congruent to Triangel OBP
7)Angle APO is congruent to Angle BPO
8)OP bisects angle APB

Reasons:
1) Given
2) Reflexive
3)
4)
5) Parallel lines form right angles
6)
7)
8) Definition of an angle bisector

and I also need help with this one:

Given:AC is a diameter of circle O. BD bisects angle ABC
Prove:OD is parallel to AC

I didn't do proofs with circles last year and have no idea how they got some of the things in the first problem. Thanks in advance!