The triangle OPA is an isosceles triangle.
Furthermore the triangle OP'A is also an isosceles triangle.
Moreover this second triangle has a common angle with the first, meaning that these two triangles are similar.
Can you say anything about what that means for OP'?
OMG! Thank you sooooooooooooooooooooo much! You're a great teacher you know!
In the last part when it says Discuss the scope and/or limitations of the general statement. I know that OP' approaches infinity as r approaches infinity and OP' approaches 0 as OP approaches infinity. Is that all? Or is there any situation in which OP' is not defined or the general statement is not working? (I know that it's not defined if OP is 0, but ...)
The only real limitation is that OP may not be zero, so the point P may not be chosen to coincide with the point O.
EDIT: Hold on! See below.