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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.

 Jan 21, 2022
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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

 

 

GEsmileyMETRY

 Jan 23, 2022

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