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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Circle has a circumference and a diameter, what is meant by length, I wonder
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It is a straight line that touches the curve such that the line is perpendicular to the radius of the curve at the point of contact.
That means that for every 5 [lengths] forward along the level, the incline rises or drops 1 [length]. [Length] can be any unit of distance. This can also be called a "20% grade" . . . Because 1/5 = 0.2 = 20% . It also tells you that the incline makes an angle of 11.3° with the level, because 0.2 is the tangent of 11.3° .
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Circle has a circumference and a diameter, what is meant by length, I wonder
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