examday

/TMUA

A point $P$ is chosen at random inside an equilateral triangle $ABC$ of side length $2$. The probability that $P$ lies in a region is proportional to that region's area.

Let $d_1,d_2,d_3$ be the perpendicular distances from $P$ to the lines $AB$, $BC$ and $CA$, respectively.

Given that $d_1\geq\sqrt3/2$, what is the probability that