Question

in the figure below, two congruent (identical) circles with centers a and b touch only at point c. if \\( \overline{ab} = 22 \\) ft, what is the circumference of circle a? leave your answer in terms of \\( \pi \\).

Explanation:

Step1: Find radius of circle A

Since the two circles are congruent and touch at point C, the distance between centers \( AB \) is equal to the sum of their radii. Let the radius of each circle be \( r \). So, \( AB = r + r = 2r \). Given \( AB = 22 \) ft, we solve \( 2r = 22 \), so \( r=\frac{22}{2}=11 \) ft.

Step2: Calculate circumference of circle A

The formula for the circumference of a circle is \( C = 2\pi r \). Substituting \( r = 11 \) ft, we get \( C = 2\pi\times11 = 22\pi \) ft.

Answer:

\( 22\pi \) ft (the box should be filled with 22)