# Staying in the triangle

Three points are chosen uniformly at random from the boundary of a square and a fourth point is chosen uniformly at random from the interior. The probability that the 4th point lies in the triangle formed by the other 3 points can be expressed as $$\frac{a}{b}$$ where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a + b?$$

×