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Circles A, B, and C are externally tangent to each other. If AB = 14, BC = 18, and AC = 18, then find the radii of each of the circles.

 Apr 26, 2021
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Let the radius of circle A be x, of B be y and of C be z. 

Now, consider the following diagram- 

From figure, 

\(x+y=14\)               ...(1)

\(y+z=18\)               ...(2)

\(z+x=18\)               ...(3)

 

Adding eq.(1), (2) and (3)

\(2x+2y+2z=14+18+18\)

\(2(x+y+z)=50\)

\(x+y+z=25\)                   ...(4)

 

Subtracting eq.(1) from (4), 

\(z=11\)

 

Subtracting eq.(2) from (4), 

\(x=7\)

 

Subtracting eq.(1) from (4), 

\(y=7\)

 

∴ Radius of circle A is 7 units, B is 7 units and C is 11 units.

 

 

~Roll the credits.

 Apr 26, 2021

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