A triangle with sides 7cm, 8cm, and 9cm is formed by connecting the centers of the three circles that are tangent to each other. Which of the following is the circumference of the largest circle?

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Answer 1 · 2018-08-09T13:14:34

#10pi" cm."#

Let #r_1, r_2 and r_3# be the radii of the circles touching

each other.

If #C_1,C_2 and C_3# are their respective centres, then, from

Geometry, we know that,

#C_1C_2=r_1+r_2, C_2C_3=r_2+r_3, C_3C_1=r_3+r_1#.

So, by what is given, we have,

#r_1+r_2=7, r_2+r_3=8 and r_3+r_1=9..........(ast)#.

Adding these, #2(r_1+r_2+ r_3)=24, or, r_1+r_2+ r_3=12#.

Utilising #(ast)# in this last eqn., we get,

# r_1=4, r_2=3 and r_3=5#.

Consequently, the circumference of the largest circle, i.e.,

#o.(r_3,C_3)# is #2pir_3=10pi" cm."#