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Question

Three circles touch each other externally. Find the radii of the circles if the sides of the triangle formed by joining the centres are 7 cm, 8 cm and 9 cm respectively.

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Solution

AB=x+y=7eq.1

BC=y+z=8eq.2

CA=z+x=9eq.3

From eq.3,

z=9x

Substituting this in eq.2

y+9x=8

xy=1eq.4

Solving eq.1 and eq.4

x=4

z=41=3

y=94=5


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