Question
Mon June 18, 2012 By: Sonali

Three circles with centres A,B,C touch one other externally. The three centres are joined to one another to form a triangle. IF AB=7cm,BC=11cmand AC=6cm find the radii of the three circles.

Expert Reply
Tue June 19, 2012
Let x, y and z be the radii of the circles with centres A, B and C.
The,
x + y = AB = 7
y + z = BC = 11 cm
z + x = CA = 6 cm
 
Adding the above three equations, we get,
2(x+y+z) = 24
x + y + z = 12
 
Solving the above obtained 4 equations, we get
x = 1 cm, y = 6 cm and z = 5 cm
which are the required radii of the circles.
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