Question

Three circles are touching each other so that the distance between each pair of centres is 8 cm, 9 cm and 13 cm. What is the radius of each circle?

Answer 1

Answer:

Let the radii of the circles be, x,y,z

then we have

x+y = 8

x+z=9

y +z=13

on adding->2x +2y +2z=30

on dividing by 2 ->

x+y+z = 3o/2 = 15

x+y+z=15

x = x + y +z-(y+z) =15-13 = 2 cm

y=x+y+z-(x+z) =15-9=6cm

z=x + y +z-(x+y) =15-8=7cm

the radii are, 2,6&7 cms