You practically have the answer already:

You have an arbitrary circle with center O and radius r, and an arbitrary point Q on that circle. And you have defined a circle with center O' (the image of O) and radius kr. So all you need to know is if Q' (the image of Q) is on the second circle. That will be true if the distance from O' to Q' is kr.

So you have defined two triangles XOQ and XO'Q'. Are they similar? If so, the ratio of the sides are all equal....

I think you can take it from there. I think if you draw diagrams for the other three problems you'll be able to do them, too.

Let me know if you have any more trouble.