Question 706416: Three circles are tangent externally to each other. The lines of centers are 12, 18 and 16 cm respectively. Find the length of the radius of each circle.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Three circles are tangent externally to each other.
The lines of centers are 12, 18 and 16 cm respectively.
Find the length of the radius of each circle.
:
Draw out the the three different size circles touching each other,
Label the distances between the centers and the radii r1, r2, r3,
derive 3 equations from this
:
r1 + r2 = 12
r1 + r3 = 16
r2 + r3 = 18
:
Arrange these equations for elimination, mult the 3rd equation by -1:
r1 + r2 + 0 = 12
r1 + 0 + r3 = 16
0 - r2 - r3 = -18
--------------------addition, eliminates r2 and r3, find r1
2(r1) = 10
r1 = 10/2
r1 = 5 is the radius of the smaller circle
then
5 + r2 = 12
r2 = 12 - 5
r2 = 7 is the radius of the middle circle
and
7 + r2 = 18
r2 = 11 is the radius of the larger circle
:
You can check this for yourself
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