Final answer:
To find the sum of the diameters of the three circles, you can set up an equation and solve for the value of r. The value of ac would be 2 times the value of r which is 12.923076.
Step-by-step explanation:
To find the sum of the diameters of the three circles, we can let the radius of circle b be r, then the radius of circle a would be 2r, and the radius of circle c would be (1/4)r.
The diameter of circle a would be 2(2r) = 4r, the diameter of circle b would be 2r, and the diameter of circle c would be 2((1/4)r) = (1/2)r.
The sum of the diameters would be 4r + 2r + (1/2)r = 6.5r.
Given that the sum of the diameters is 42, we can set up the equation:
6.5r = 42
Solving for r:
r = 42 / 6.5
= 6.461538
Therefore, the value of ac would be 2(6.461538) = 12.923076.