Q. 12 C4.6( 5 Votes )

# 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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