Circles A, B, and C are externally tangent to each other. If AB = 14, BC = 18, and AC =\(28\), then find the radii of each of the circles.
We can first label the radii of each of the circles to a variable.
Radius of circle A = x
Radius of circle B = y
Radius of circle C = z
Now we can write some equations:
\(x + y = 14\)
\(y + z = 18\)
\(x + z = 28\)
Then we add up the three equations and divide by two to get:
\(x + y + z = 30\)
We take the equation above us (equation4) and subtract it from equation2 to get x = 12.
We take the equation above us (equation4) and subtract it from equation3 to get y = 2.
We take the equation above us (equation4) and subtract it from equation1 to get z = 16.
So the radius of circle A is 12
So the radius of circle B is 2
So the radius of circle C is 16
GEMETRY