Question

На какое найбольшее число различных частей могут разбивать пдоскость три окружность?

Answer 1

На 8 частей могут разбивать плоскость 3 окружности:

Answer 2

Maximum Number of Regions Formed by Three Circles on a Plane

The maximum number of different parts into which a plane can be divided by \( n \) circles is given by the formula \( 1 + n + \frac{{n(n-1)}}{2} \).

For three circles, the maximum number of regions they can divide the plane into is calculated as follows: \[ 1 + 3 + \frac{{3(3-1)}}{2} = 1 + 3 + \frac{6}{2} = 1 + 3 + 3 = 7 \]

Therefore, the maximum number of different parts three circles can divide a plane into is 7.