What is the Length of a Rope When Two Pipes are Tied Together?

[Icelove]

Homework Statement

The problem is pretty long but it is easy except one part where I need to calculate the length of a rope where 2 pipes are tied together tightly. We can reduce this to 2 dimensions so I drew a rough sketch of it. I didn't quite succeed with the the perfect drawing but you get the idea.

Here's the sketch

So the informations we are given that the diameter of the bigger pipe's is 90cm, the smaller one's is 30cm.

Homework Equations

i = r*a(rad)
K = 2*r*pi

The total cc of the big circle is:~282.7cm ,and the smaller one is: ~94.2 cm

The Attempt at a Solution

I tried with Pythagoras' theorem but I realized with this kind of calculation, I get an approximation and not real solution.


I then figured that I have to calculate the circumference of both circles then substract the length of the arc. Then I still have to find the distance between the two circles connected by the bridges.

Since we only have the information of the radiuses I was thinking that we have to find a ratio between the circles and then can get the arc. I tried simplify it by creating 2 equal sized circles then shrinking one of them, but I got confused and couldn't get my ratios.


So forum, can you lead me to success?

 

[tiny-tim]

Hi Icelove!

The straight parts will be the common tangents of the two circles, so draw the two radii: you know their lengths, and the distance between the centres, and you know that the tangent is perpendicular to the radii …

from that, you can find the length of the tangent, and the angle between the radii and the line through the centres.

 

[Icelove]

tiny-tim, you are opening my math eye. I love you, thanks AGAIN. :)