SOLUTION: Three circles C1,C2,C3 are externally tangent to each other. Center-to-center distances are 10 cm between C1 and C2 , 8 cm between C2 and C3 , and 6 cm between C3 and C1. Determi

When two circles touch externally, the distance between their center is the sum of their radii.

It gives you the system of three equations

a + b = 10,     (1)
a + c =  8,     (2)
b + c =  6.     (3)

where a, b and c are the radii of the three circles with the centers A, B and C respectively.


To solve the system, first add all the three equations. You will get

2a + 2b + 2c = 10 + 8 + 6 = 24,

which implies 

a + b + c = 12.   (4)


Now subtract equation (3) from equation (4) (both sides). You will get c = 12-10 = 2.

    Subtract equation (2) from equation (4) (both sides). You will get b = 12-8 = 4.

Finally, subtract equation (1) from equation (4) (both sides). You will get a = 12-6 = 6.


Now the area under the question is   = 175.84 cm^2.