Well, if the objects you are detecting a collision between are both spherical, then it's quite simple to detect if they are in contact. Just take the distance between the objects with the formula
which is a simple derivative of Pythagora's theorem:
distance = sqrt(x*x + y*y)
There's actually a C99 function called hypot() which does just this, in a better way -- because if you just used the literal equation, x*x or y*y might overflow. But it's C99 only as far as I am aware.
You can derive simple formulae for other collisions as well. For example, if the arrow was a sphere and the ground was flat, you would just take the vertical component of their separation and use that.
Collision detection can get a lot more complicated that this, of course. You might want to post some more information -- for example, what is the circular arrow colliding with?