Need some help with some pre calc summer math questions

Here are the questions I am having trouble with, any help would be appreciated, thanks. (Cool)

2. Let chords AB and CD of circle O intersect at point E. If BE = x , EA = 3x -1, DE = x -1, and CE = 4x ,

find the lengths of these chords.

3. From a point P outside of circle O, let PRbe tangent to the circle at R and let secant PM intersect the circle at

M and N (with M between P and N). If PM = 9 and MN = 3, find PR.

4. From a point P outside of circle O, let PR and PS be tangent to the circle at R and S respectively. Find OP if the

radius of the circle is 5 and PR = 13.

8. If ABCD is a rectangle and P is any point in its interior, prove that AP2+PC2=PB2+PD2.