1. **Problem statement:** Given seven points on a plane, no three of which are collinear, we want to find how many polygons can be drawn using these points as vertices. 2. **Key idea:** A polygon is formed by choosing at least 3 points from the given points. Since no three points are collinear, every subset of points with size 3 or more forms a polygon. 3. **Formula:** The number of polygons is the sum of combinations of 7 points taken $k$ at a time for $k=3$ to $7$: $$\sum_{k=3}^{7} \binom{7}{k}$$ 4. **Calculate each term:** - $\binom{7}{3} = \frac{7!}{3!4!} = 35$ - $\binom{7}{4} = \frac{7!}{4!3!} = 35$ - $\binom{7}{5} = \frac{7!}{5!2!} = 21$ - $\binom{7}{6} = \frac{7!}{6!1!} = 7$ - $\binom{7}{7} = 1$ 5. **Sum all:** $$35 + 35 + 21 + 7 + 1 = 99$$ 6. **Answer:** There are $\boxed{99}$ polygons that can be drawn from the seven points with no three collinear.