Hint #1: The mouse or the cheese can be less than 10cm from the polygons
Hint #2: Be careful of your first segment from the mouse or the last segment from the cheese. If you do not check correctly, they might cross a polygon. For example, think of the case of a very thin rectangle with the long side called A and a mouse that is less than 10cm from the rectangle. You have to make sure that the mouse runs to side A not the side opposite to A.