0
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.
Add your answer:
Earn +20 pts
What is meant by tangent to a curve at a point?
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.
What is meant by incline of 1 in 5?
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° .
What is the formula for length of a circle of radius 0.11M?
Circle has a circumference and a diameter, what is meant by length, I wonder
What is the length of a side of a square if width is 4 cm and length is 6 cm?
well if you have 6cm and 4cm it's not a square, it's a rectangle. you also mentioned that the length is 6cm. if you meant the area, this is length by width which is 24cm2. If you meant the perimeter this is 2w+2l, which is 20cm
What is meant by length of an interval?
If suppose a tea break is given in a discussion session, say for 15 minutes, then this duration 15 minutes is the length of the interval. If we have to increase that length then we may make it to be 20 minutes.
What is meant by tangent to a curve at a point?
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.
What is meant by incline of 1 in 5?
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° .
What is meant by grazing ray?
it is the ray produced when the light ray fall on a medium with angle=90 and this ray produced becomes a tangent to the separating surface.
What is meant by oblique transverse and triangular ridges?
These are terms that refer to specific anatomical features of teeth. These terms are only important to dental professionals.
What is the formula for length of a circle of radius 0.11M?
Circle has a circumference and a diameter, what is meant by length, I wonder
What is the length of A PYRAMID?
The length of a pyramid is one of the sides of the base, typically the longer one. (If you meant it literally, then the length of "A PYRAMID" is 9.)
What is the length of a side of a square if width is 4 cm and length is 6 cm?
well if you have 6cm and 4cm it's not a square, it's a rectangle. you also mentioned that the length is 6cm. if you meant the area, this is length by width which is 24cm2. If you meant the perimeter this is 2w+2l, which is 20cm
What is meant by the payback period?
Something is meant by the payback period. It is the length of time taken to recover the cost of an investment. This is what is meant by the payback period.
Which is bigger a computer screen or a science text book?
if you meant width then a computer if you meant thickness a since textbook i you meant length then a textbook
What does it mean to speak in riddles?
To speak in riddles at times is a response to a question that is meant to confound and perhaps confuse the listener with a long speech that rambles and goes off on a tangent. It can be fillibustering. It can be jest. It can mean speech meant to not answer the question directly or at all.
What does mean and meant have in common?
mean can also mean rude but if you are looking for something in common with meant....mean is a present tense for meant and meant is past tense... examples ex: what do you mean? ex: he meant that he had 4 dogs, not four cats.
What was the most common object used as a basis for measuring length?
The most comon ways are using rulerAnswer:It depends on what is meant by "most common". If most commont means :which object measures the most length in any time period" it is probably the odometer in a cars as each measures about 10k km a year.If th emphasis is "basis" then it is the stanfard objects used for establishing length in the SI (metric) units.system
