Question

Select point B, and drag it. As you drag B, circle AB changes. Verify that you can make circle AB coincide with AC. Return B to its approximate initial position. When circle AB coincides with circle AC, what do you notice about the regions CAD and EAF? In terms of similarity, what does your observation imply about the relationships among the lengths of the radii of AB and AC and the lengths of arc EF and arc CD? Write the relationship in the form of a proportion, and explain how it follows from your observation.

Answer 1

When AB coincides with AC, the boundary of EAF maps exactly onto the boundary of CAD, implying that EAF dilates into CAD. So, the boundaries of EAF and CAD are similar.

The proportional relationship may be stated in different forms, but should be equivalent to this equation:

radius of Ab/ radius of Ac= length of arc EF/ length of arc CD

Explanations will vary, but should be based on the similarity of EAF and CAD. The proportional relationship follows from the fact that corresponding pairs of lengths in two similar figures have the same ratio.

Explanation:

This is the exact answer so make sure you change it up a little.

Answer 2

When AB coincides with AC, the boundary of EAF maps exactly onto the boundary of CAD, implying that EAF dilates into CAD. So, the boundaries of EAF and CAD are similar.

The proportional relationship may be stated in different forms, but should be equivalent to this equation:

the radius of AB /radius of AC= length of arc EF/length of arc CD

The proportional relationship follows from the fact that corresponding pairs of lengths in two similar figures have the same ratio.

Explanation: