Astraight path goes through the woods. a deer walks into the woods and keeps walking on the path. at what point does the deer begin to leave the woods?

Once it has reached the half way point; i.e. once it has coverd 1/2 of the total length of the path the lies within ithe woods. Another way to think of it is to image that the woods are circular and the deer is at the exact center. To get there it had to go 1/2 the diamter inwards and any direction it moves is closer to the edge, ie. outward. 

None of the options you showed are it.