A few days ago
punkrocker490

# I have 2 concentric circles and a tangent, can you help me find the surface area?

Okay, there’s an inner circle made of bronze and an outer one made of silver, it’s a coin. The tangent is on the top of the inner circle and when measured is 23 units from intersection to intersection with the edge of the outer circle. Can anyone give me a starting place and help me bust this one?

A few days ago
Twiggy

Let the radius of the smaller circle be r cm, and that of thhe larger be R cm. Draw the radius of the smaller circle from the centre of the circle to the point of contact with the tangent.Draw the radius of the larger circle from the centre to one end of the point of contact with the larger circle. you now have a rt angled triangle of hypoteneuse R, and the other two sides of 11.5 cm and r cm.

By Pythag in this triangle, R^2 – r^2 = [11.5]^2

you don,t need to find R, in fact you can`t, but the area you need is given by:

A = pi[R^2 – r^2]

= pi[11.5]^2, and I`m sure that you can work this out ? Hope this helps, Twiggy

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A few days ago
Anonymous
If the length of 23 is the only measurement you have, there is no unique solution. The fact that it is a tangent to the inner circle is no help when you have no measurements telling you about the inner circle.

If, for example, the radius of the inner circle were known to be r, then you could join the point of contact of the tangent to the centre of the circles, and join the centre to the two extremities of the tangent.

That would give you two right-angled triangles, each with one side equal to 23/2 and the other equal to r.

Then you could use Pythagoras’ theorem to find the radius of the larger circle, which would be the hypotenuse. With that, you could calculate the area.

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A few days ago
ballerinagirl
neopets cheater haha.
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