Question

in the figure below, two congruent (identical) circles with centers a and b touch only at point c. if \\( \overline{ab} = 12 \\) ft, what is the circumference of circle a? leave your answer in terms of \\( \pi \\).

Explanation:

Step1: Determine the radius of Circle A

Since the two circles are congruent and touch at point C, the distance between their centers \( AB = 12 \) ft is equal to the sum of their radii. Let the radius of each circle be \( r \). Then \( AB = r + r = 2r \). So, \( 2r = 12 \), which gives \( r=\frac{12}{2}=6 \) ft.

Step2: Calculate the circumference of Circle A

The formula for the circumference of a circle is \( C = 2\pi r \). Substituting \( r = 6 \) into the formula, we get \( C = 2\pi\times6 = 12\pi \) ft.

Answer:

\( 12\pi \)