Please help me with this problem ASAP!

[TheShadow]

Hello everyone


I'm having a bit of difficulty solving this problem, can someone please solve it for me? And explain how you did it? I'd be forever grateful. There are more problems like this, so if you could fully solve this so I have a guideline of sorts to deal with the rest, that would be amazing

The problem is in the attachment, have a look.


Thanks!

 

[Deleted member 4993]

Hello everyone


I'm having a bit of difficulty solving this problem, can someone please solve it for me? And explain how you did it? I'd be forever grateful. There are more problems like this, so if you could fully solve this so I have a guideline of sorts to deal with the rest, that would be amazing

The problem is in the attachment, have a look.


Thanks!

Please share your work with us ...

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

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[TheShadow]

Well the thing is, I'm struggling with this problem and there are many more almost identical to this. I need to do them ASAP (exam prep) and so I was hoping they could be solved by someone and shown how it was done, so I could use it as a guideline of sorts for all the rest. I understand though, that you can't just give answers.

So far, I managed to find the angle a by using cos(α)=R−d2/R. I can't find the distance L though. Please help?

Thanks!

 

[Ishuda]

Well the thing is, I'm struggling with this problem and there are many more almost identical to this. I need to do them ASAP (exam prep) and so I was hoping they could be solved by someone and shown how it was done, so I could use it as a guideline of sorts for all the rest. I understand though, that you can't just give answers.

So far, I managed to find the angle a by using cos(α)=R−d2/R. I can't find the distance L though. Please help?

Thanks!

Just so we can talk about co-ordinates, let the origin of our co-ordinate system be at point A = (0,0). The bottom channel is then the line
b(x) = 0
and the top channel is the line
t(x) = 30
The line b is tangent to the circle whose center is at O = (0,75) and radius is 75 at x=0. The first part of join [interconnection] is part of that circle. The second part of the join is part of a circle whose center is at C = (L, 30-75) = (L, -45) and that circle is tangent to line t at point B = (L, 30). Let line y be the line that passes through points O and C (note that C is not labeled on the image). Then the two circles are tangent to each other midway between their centers on line y.

That should be enough information to establish what you need. For example, consider the triangle with corners (vertices) at C, O, and (0, -45). What is the distance between C and O?

BTW: Check the numbers - I found myself using 18 instead of 30 for d and, although I think I caught it all, I may not have.