SOLUTION: The center of three circle that are tangent to each other are connected to form a triangle that has a measurement of 4cm, 6cm, and 8cm. Find the measurement of the biggest circle.

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Question 1082188: The center of three circle that are tangent to each other are connected to form a triangle that has a measurement of 4cm, 6cm, and 8cm. Find the measurement of the biggest circle.
Answer by ikleyn(52884) About Me  (Show Source):
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The highlight%28cross%28center%29%29 centers of three highlight%28cross%28circle%29%29 circles that are tangent to each other are connected to form a triangle
that has highlight%28cross%28a%29%29 side highlight%28cross%28measurement%29%29 measurements of 4cm, 6cm, and 8cm. Find the highlight%28cross%28measurement%29%29 radius of the biggest circle.
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Let the radii of these circles be "a", "b" and "c", in increasing order.

Then you have these equations

a + b = 4,   (1)
a + c = 6,   (2)
b + c = 8.   (3)

Add the three equations, (1),(2) and (3), You will get

2a + 2b + 2c = 4 + 6 + 8 = 18,

which  implies

a + b + c = 9.   (4)

Now subtract eq(1) from eq(4). You will get

c = 9-4 = 5.


Next, subtract eq(2) from eq(4). You will get

b = 9-6 = 3.


Finally, subtract eq(3) from eq(4). You will get

a = 9-8 = 1.


Thus you found the radii. They are  a= 1,  b= 3  and  c= 5.


The biggest circle has the radius of 5 cm.

Solved.