# circle pattern problem

## Suggestion:

This pattern is partially constructed below. You may drag some points to adjust the radii of the circles. This may be useful for solving the problem or generating other patterns.

In order to make the required pattern with 4 centres, what should be the relation between the radius of a larger circle (R) and that of a smaller circle (r)?

## Extension:

Would you like to solve similar problems like the following?

- How would you describe these patterns?
- Can you tell the relation between the radius of a larger circle (R) and that of a smaller circle (r) in each case?

What is the relation between R and r in this figure? (with 3 centres)

What is the relation between R and r in this figure? (with 5 centres)

The following figure may be useful for further exploration.

What is the relation between R, r and n (number of centres)?