Question 763342: three circles are tangent externally.the distances between their centers are 23 inches,25 inches,20 inches.find their radii.
Found 2 solutions by ramkikk66, lwsshak3:
Answer by ramkikk66(644)   (Show Source):
You can put this solution on YOUR website! If the 3 circles are externally tangential to each other, then it means that the line connecting their centers passes through the tangential point.
Which means that the distance between their centers is anyway equal to the sum of their radii.
So, if x, y, z are the radii of the 3 circles,
x + y = 23 ---- eqn(1)
y + z = 25 ---- eqn(2)
x + z = 20 ---- eqn(3)
Adding the above 3 equations, we get 2*x + 2*y + 2*z = 68, or x + y + z = 34 ---(eqn 4)
From (1) and (4), we get 23 + z = 34 or z = 11
From (2) and (4), we get 25 + x = 34 or x = 9
From (3) and (4), we get 20 + y = 34 or y = 14
So the radii of the 3 circles are   
:)
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! three circles are tangent externally.the distances between their centers are 23 inches,25 inches,20 inches.find their radii.
***
let x=radius of 1st circle
let y=radius of 2nd circle
let z=radius of 3rd circle
..
x+y=25
y+z=23
x+z=20
..
x+y=25
z+y=23
subtract
x-z=2
x+z=20
add
2x=22
x=11
y=25-x=14
z=20-x=9
radius of 1st circle=11 inches
radius of 2nd circle=14 inches
radius of 3rd circle=9 inches
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