Given an angle AOB and a point M inside it, construct a segment PQ such that
- M is the midpoint of PQ
- P is on side OA
- Q is on side OB
So i've been thinking about this problem and of course the best and easiest case i can construct for, is when M lies on the angle bisector of AOB but of course there's a construction that includes for ANY arbitrary point of M.
The only idea i have in my head, is that this line segment PMB has its average located at M. So in general, M is the line's average length.
Question: How should i go about solving this construction problem? We are given the tools of circle inversions, homothety, isometries constructing trivial things such as perpendiculars, angle bisectors etc...