Maximum number of points of intersection of 6 circles is

Options

A. 30
B. 28
C. 15
D. none of these

Answer

To find the maximum number of points of intersection of 6 circles, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Circle Intersections**:
Each pair of circles can intersect at most at 2 points. Therefore, we need to determine how many pairs of circles can be formed from 6 circles.

2. **Calculating Pairs of Circles**:
The number of ways to choose 2 circles from 6 is given by the combination formula:
\[ \text{Number of pairs} = \binom{n}{r} = \frac{n!}{r!(n-r)!} \]
Here, \( n = 6 \) (the total number of circles) and \( r = 2 \) (the number of circles we are choosing).
\[ \binom{6}{2} = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = 15 \]

3. **Calculating Maximum Intersections**:
Since each pair of circles can intersect at 2 points, the total maximum number of intersection points is:
\[ \text{Total intersections} = \text{Number of pairs} \times 2 = 15 \times 2 = 30 \]

4. **Final Answer**:
Therefore, the maximum number of points of intersection of 6 circles is **30**.

### Summary:
The maximum number of points of intersection of 6 circles is 30.

---