<p>Find the maximum number of points of intersection of 6 circles.</p>
Step-by-Step Solution
Key Concept: Any two distinct circles can intersect at most at 2 points. With 6 circles, we need to count maximum pairs and multiply by 2, ensuring no three circles meet at the same point (general position assumption).
<p><strong>Step 1:</strong> Recognize that two distinct circles can intersect at a maximum of 2 points.</p><p><strong>Step 2:</strong> Calculate the number of ways to choose 2 circles from 6 circles (number of pairs): $\binom{6}{2} = \frac{6 \times 5}{2} = 15$</p><p><strong>Step 3:</strong> Since each pair of circles contributes a maximum of 2 intersection points, multiply: $15 \times 2 = 30$</p><p><strong>Step 4:</strong> This assumes general position (no three circles pass through the same point), which gives the maximum number of intersections.</p><p>∴ Answer: <strong>30</strong></p>
Correct Answer: 30