Context

I have a bus, at position {x, y}. It is going in a direction d, in radians.

I need to draw two arcs that shows its turning radius. Let's keep to one arc.

I need to center the arc some distance i from {x,y}. Arc start and end are not important.

Of course, the arc has a radius, but its not important.

Problem

Distance i, which is really {dx,dy}, becomes "skewed" when the bus turns.

When it is as I drew it previously, dy=0, dx=i. Easy.

In the general scenario,

dx and dy are unknown and to be determined.

I know there's a cos and/or sin in there, but I feel like i've tried every possible combination!

I need to

a) have the formulas for dx and dy; and

b) understand how/why it works so I can do the second left-wheel arc.