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To determine how many different quadrilaterals can be drawn using 7 points on a circle, we need to calculate the number of ways to select 4 points from the 7 points. 

The formula for selecting \( r \) points from \( n \) points is given by the combination formula:

\[
C(n, r) = \frac{n!}{r!(n-r)!}
\]

Here, \( n = 7 \) and \( r = 4 \). Substituting these values:

\[
C(7, 4) = \frac{7!}{4!(7-4)!} = \frac{7 \cdot 6 \cdot 5 \cdot 4!}{4! \cdot 3 \cdot 2 \cdot 1} = \frac{7 \cdot 6 \cdot 5}{3 \cdot 2 \cdot 1} = 35
\]

Thus, **35 different quadrilaterals** can be drawn using these endpoints.

### Would you like a step-by-step breakdown of the formula or further explanation? Let me know!

Here are 5 questions you might find helpful:
1. How does the combination formula work in general?
2. Why does this problem involve combinations rather than permutations?
3. What if there were 8 points instead of 7—how would the answer change?
4. Can this approach be applied to draw polygons with more than 4 sides? How?
5. What are the geometric properties of quadrilaterals formed on a circle?

**Tip:** Always consider whether a problem involves combinations (unordered selection) or permutations (ordered selection) to apply the correct formula.

There are 7 points on a circle, as shown. How many different quadrilaterals can be drawn using these endpoints?

Discover how to calculate the number of quadrilaterals that can be formed using 7 points on a circle. Learn about the combination formula and geometric principles involved in solving this problem, suitable for Grades 9-11.

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