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Two circles of diameters 2 cm and 5.6 cm are such that the distance between their centres is 8.2 cm. What is the length of a common tangent to the circles that does not intersect the line joining the centres?
AB is a common tangent
Construct EC parallel to AB
Now Triangle EDC is a right angled triangle in which DC = 8.2 cm and ED = AD - BC = 2.8-1=1.8 cm (BC=AE)
EC = $$\sqrt{\left(DC\right)^2-\left(DE\right)^2}=\sqrt{8.2^2-1.8^2}=\sqrt{\ 64}=8$$ cm
So, length of common tangent will be equal to EC = 8 cm.
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