SOLUTION: 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.

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
RELATED QUESTIONS
three circles are tangent to each other externally. The distance between their centers... (answered by Alan3354)

Three circles of radii 2, 4, and 6 are tangent to each other externally. Find the area... (answered by Fombitz)

Three circles with centers A, B, and C are externally tangent to each other as shown in... (answered by Alan3354)

the distance between the centers of the three circles which are mutually tangent to each... (answered by greenestamps)

Circles A, B, and C are externally tangent to each other. AB= 10 cm, BC= 12cm, and CA=16. (answered by Alan3354)

Three circles A, B and C are externally tangent to each other. The length of lines... (answered by greenestamps)

Three circles are mutually tangent to one another externally. Their centers are connected (answered by ikleyn)

The vertices R, S, T of the right triangle RST are the centers of 3 circles. The circles... (answered by Theo)

Find the area contained between three circles of radius 20 cm. each of which is... (answered by greenestamps)