Lately I have become hooked on the game Euclidea. One of the problems gives a triangle and asks you to construct the incenter, or as it is put, "the intersection of angle bisectors."
It is stated that it should only take six steps. Steps are in the mode of the straightedge and collapsible compass constructions at the beginning of Baby Hartshorne: use of the ruler to construct a line or line segment and use of the compass to construct a circle are counted. Extending lines or constructing points at previously constructed intersections are not.
The obvious solution
has sadly been my best effort: bisect two of the triangle's angles (3 circles and 1 line each) and mark the intersection of the two lines.
Any help is appreciated.
Your construction is fine, but you can spare two circles if you use the points that are already there, see diagram below.