A point P is uniformly chosen inside a regular hexagon of side length 3. For each side of the hexagon a line is drawn from P to the point on that side which is closest to P. The probability that the sum of the lengths of these segments is less than or equal to 9√3 can be expressed as a/b where a and b are coprime positive integers. What is the value of a+b?

Question

Details and assumptions
The side of the hexagon is a line segment, not a line.

Note that the 6 closest points are always distinct, hence we will have 6 distinct line segments.

Answer 1

vertices of a hexagon. The line segment joining the two points forms one of the sides of the hexagon. Which statement explains the segment formed by these endpoints?