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(a) Let $ABC$ be an equilateral triangle, centered at $O.$ A point $P$ is chosen at random inside the triangle. Find the probability that $P$ is closer to $O$ than to any of the vertices. (In other words, find the probability that $OP$ is shorter than $AP,$ $BP,$ and $CP.$)



(b) Let $O$ be the center of square $ABCD.$ A point $P$ is chosen at random inside the square. Find the probability that the area of triangle $PAB$ is less than half the area of the square.

Sagot :

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