Okay, so here's the situation:

I have three actors that may be placed in any possible relation to each other, but they don't move. Thus, they are basically the three points of a static triangle. For each of these points, I need to find a circle that is tangent to the shortest adjacent side of the triangle at its midpoint, and also tangent to the other adjacent side (but not necessarily at the midpoint). Basically, I need a curve that fits nicely into each corner of the triangle.

I've been going back to my trig textbooks to try to pull this together, but so far the only leads on a solution that I've found seem like they'd be pretty computationally expensive (I may need to do this calculation a few times for each level of the game). What's the most efficient way to calculate the center point and radius of these circles?

Thanks for any help you can offer!