How to reduce the length of sides AB and BC of a triangle ABC by a given amount g such that the median (at X, previously at B) remains the same?
The new distances, in relation to the old ones:
dist(A, X) + dist(X, C) = dist(A, B) + dist(B, C) - g
EDIT
The equation holds for 0 < g < dist(A, B) + dist(B, C) - dist(A, C) . X can be at any point in the median, depending only on the given g.
I am looking for a formula describing X in function of g.
