Q12 of 31 Page 218

In the adjoining figure, three circles with centre A, B, C touch one another externally. If AB = 5 cm, BC = 7 cm and CA = 6 cm, let us find the length of radius of circle with centre A.

Let radius of circle with centre A be x, with centre B be y and with centre C be z


x + y = 5


⇒ y = 5-x …Equation(i)


y + z = 7


Putting the value of y from Equation (i) in the above equation


5-x + z = 7


⇒ z – x = 2 …Equation (ii)


z + x = 6 …Equation (iii)


Adding Equation (ii) and (iii) we get


2z = 8


⇒ z = 4 cm


Putting the value of z in Equation (iii) we get


4 + x = 6


⇒ x = 2 cm


The length of radius of circle with centre A = 2 cm


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