Question

Point P is chosen at random in a circle. If a square is inscribed in the circle, what is the probability that P lies outside the square?

Answer 1

The probability that the point P lies outside the square is;1 - (2/π)

How to choose a point in a circle?

If a is the radius of the circle, then;

Area of the inscribed square = 2a²

Now, area of the circle is;

Area of circle = πa²

Thus, probability that the point lies outside the square is;

Area of between circle and square/area of circle

Area between circle and square = πa² - 2a² = a²(π - 2)

Thus;

P(the point lies outside the square) = a²(π - 2)/πa² = (π - 2)/π = 1 - (2/π)

Read more about Circles at; brainly.com/question/1559324

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