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AB is a common tangent of circles C, D, E and F. Suppose that AC = 12, DB = 9 and AE = BF = 3. If the midpoint of EF is the center of a circle that is tangent to both circles E and F, what are the possible values for its radius?

AB is a common tangent of circles C, D, E and F. Suppose that AC = 12, DB = 9 and-example-1

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see the figure below to better understand the problem

Find out the length of the side AB

Applying the Pythagorean Theorem

AB^2=3^2+21^2

AB^2=450

AB=15√2 units

EF=AB

so

EF=15√2 units

Subtract the radius of circle E and circle F

The diameter of a circle that is tangent to both circles E and F is

D=15√2-3-3=(15√2-6) units

To find out the radius, divide the diameter by 2

r=(15√2-6) /2 units

r=7.6 units

therefore

The radius is 7.6 units

AB is a common tangent of circles C, D, E and F. Suppose that AC = 12, DB = 9 and-example-1
User Roman Orac
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