A circle with a radius of 2 units is perfectly inscribed in a square. The sides of the square touch the circle at exactly four points. If a point is chosen at random inside the square, what is the probability that the point is also inside the circle?
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π/4
π/2
1/π
4/π
The area of the square is (2r)^2 = 4. The area of the circle is πr^2 = 4π.
Therefore, the probability of a point chosen at random inside the square also being inside the circle is the ratio of the area of the circle to the area of the square, which is:
(4π) / 4 = π
So, the probability is π/4.