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Two circles of diameters 2 cm and 5.6 cm are such that the distance between their centers is 8.2 cm. What is the length of a common tangent to the circles that does not interest the line joining the centers?

Two circles of diameters 2 cm and 5.6 cm are such that the distance between their centers is 8.2 cm. What is the length of a common tangent to the circles that does not interest the line joining the centers? Correct Answer 8 cm

Formula used:

Length of a common tangent to the circles = √

where d = distance between the centres of the circle

and r1 and r2 are the radius of the circle

Calculation:

r1 = 1 cm

r2 = 5.6/2 = 2.8

Length of a common tangent to the circles = √ = √(8.2)2 - (1.8)2 = √(8.2 + 1.8)(8.2 - 1.8) = √(10 × 6.4) = 8 cm

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