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- Use similarity to generalize the results.
We know that all circles are similar to each other.
Suppose a circle has a radius of units.
- The scale factor of this circle (with radius ) and the circle with radius 1 is:
- You know how a scale factor affects area measures:
If the scale factor is , then the area is times as much.
1. Explain how we know that all circles are similar to each other.
(Hint: Think about similar measurements that circles may have.)
2. If the scale factor of a circle is , how does this relate to a circle’s area?