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.
+526 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.
