Question 64

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?

Solution

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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