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Calculate the length of a direct common tangent of two circles of radii 3cm and 8cm with their centres 13cm apart?
soln.-
Consider two circles of radii 8 cm and 5 cm with center D and C respectively.
It is given that, distance between the center of the circle is 13 cm.
∴ DC = 13 cm
Let AB be the length of common tangent.
From above figure, it is quite clear that AB = CE = x cm (let) and
DE = AD - AE = 8 cm - 3 cm = 5 cm
In right triangle DCE, by pythagoras theorem,
DC2 = DE2 + CE2
⇒ 132 = 52 + x2
⇒ x2 = 169 - 25
⇒ x2 = 144
⇒ x = √144 cm = 12 cm
Hence, AB = CE = x cm = 12 cm
Hence, the length of direct common tangent is 12 cm.
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