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- #1

- Thread starter Andrei
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- Thread starter
- #1

- Jan 17, 2013

- 1,667

It is not clear what is d from the picture .

- Mar 4, 2013

- 188

It is not clear what is d from the picture .

I am also interested in the solution.The center of the fourth circle is situated at given distancefrom that line.d

I am also interested in the solution.The center of the fourth circle is situated at given distancefrom that line.d

Edit:

I also don't know where to start with this one.

But I really wonder why this works for all proportions in which the centre of the biggest circle is divided into.

It looks like d/2 is the radius of the 4th circle for all proportions (by my visualisation).

But to start working on it,I think I have to get to paper and pencil.

At first I would be looking for the case in which the centre of the big circle is divided into two equal parts as I assume it is easier to understand.

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- #4

- Feb 7, 2012

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The centers of three circles are situated on a line. The center of the fourth circle is situated at given distance d from that line. What is the radius of the fourth circle if we know that each circle is tangent to other three. Please give me a hint, if you can. Answer: \(\displaystyle d/2.\)

Now you have to bring in the distance $d$. I think the neatest way to do that is to use the fact that the area of triangle $O_2O_3O_4$ is $\frac12d(r_2+r_3)$. It is also given by Heron's formula in terms of $r_2,\ r_3,\ r_4$. Compare the two results and you will find that $r_4 = \frac12d$.

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