The size of the piano can be changed by moving the two red points in the upper left.
The piano can be moved along the left wall of the vertical corridor using the point A.
The minimum width of the two corridor is adapted to the piano's position. They are determined by the following geometric argument: Any 2D motion is a rotation around a point. We need the rotation centre of the current motion/rotation of the piano. Since the two points A and B are moving along the walls the vertical and horizontal line need to be tangents at two concentric circles (white), why the centre C is the intersection of the lines perpendicular to the two walls through A and B. Since the piano is rotating around C the point D, which is closest to the centre of rotation, defines the minimum width of one corridor, given the with of the other corridor.