Hi.
You can achieve this by using Sin and Cos functions, it's easy:
Lets supose you have your "anchor" point at (10, 10) and want to put
your object at a distance from the anchor of 5 units.
First rotate your object the amount you want (for all my explanation i
will work in radians), lets supose the object must be on the right of
the anchor initially, a PI / 2 rotation must be applied (90º), if it
must be on top of the anchor point it will be a rotation of 0rad (0º),
under it a rotation of PI (180º), etc...
Once the object is rotated, to calculate the position of the object
you must set it at (10, 10) + (Math.Sin(angle) * distance,
Math.Cos(angle) * distance), in our example it will be (10 +
(Math.Sin(Math.PI / 2d) * 5), 10 + (Math.Cos(Math.PI / 2) * 5)).
I'm doing this in my head, i don't remember if the objects rotation
must be inverted (multiply it by -1 and it's ok), try it by yourself.
Hope it helps.