Point Inside a Triangle
Combinatorics · 28th PMO Qualifying Stage
Let $\triangle ABC$ be a right triangle with legs of lengths 6 and 8. A point $P$ is chosen uniformly at random from the interior of $\triangle ABC$. What is the probability that the distance of $P$ from at least one side of the triangle is at most 1?
A$\dfrac{1}{2}$
B$\dfrac{5}{8}$
C$\dfrac{2}{3}$
D$\dfrac{3}{4}$