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December 26th, 2011, 03:38 AM   #1
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The minimum radius

I have the problem presented in the attached image.
Does someone know how can this be solved?

Thank you.
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December 26th, 2011, 04:47 AM   #2
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Re: The minimum radius

I posted a image with the wrong Q angle.
The correct image is attached here.
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December 26th, 2011, 05:16 AM   #3
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Re: The minimum radius

Please show WHOLE diagram.
Also hard to tell what's "parallel"; AB is parallel to CD, right? So how can they be parallel to different lines?
By "fitting", do you mean corners B and C will be on larger circle's circumference?
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December 26th, 2011, 06:45 AM   #4
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Assuming that it's CB that's parallel to Y, not CD, try using coordinate geometry and trigonometry; r2 equals the longer of OC and OB.
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December 26th, 2011, 07:39 AM   #5
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Re: The minimum radius

Yes, the text is wrong. Should be "CB is parallel to Y" not "CD is parallel to Y".
By fit I mean C touches the larger circle and AD is tangent to the smaller circle.
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December 26th, 2011, 07:51 AM   #6
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Re:

Quote:
Originally Posted by skipjack
Assuming that it's CB that's parallel to Y, not CD, try using coordinate geometry and trigonometry; r2 equals the longer of OC and OB.
Yes, but I have no ideea how to calculate OC.
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December 26th, 2011, 08:42 AM   #7
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Re: The minimum radius

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December 26th, 2011, 08:47 AM   #8
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Re: The minimum radius

Quote:
Originally Posted by Denis
Please show WHOLE diagram.
Sorry, didn't notice the whole diagram was available by "dragging" ......
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December 26th, 2011, 09:18 AM   #9
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Re: The minimum radius

You could have simply stated: rectangle ABCD has horizontal side AB = x and vertical side BC = y.
That's what I'm doing(!) in this solution; also using r instead of your r1:

Make E the point where the radius line meets AD; so angle AOE = Q

Let a = AE: you can easily calculate length of a, since you have side r and angle Q (right triangle).

Extend OE to OF (F on BC).
You now have right triangle OFC: OF = r + x, CF = y - a
So length of OC (the longer radius) = SQRT[(r + x)^2 + (y - a)^2]
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December 26th, 2011, 09:40 PM   #10
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Re: The minimum radius

Quote:
Originally Posted by Denis
You could have simply stated: rectangle ABCD has horizontal side AB = x and vertical side BC = y.
That's what I'm doing(!) in this solution; also using r instead of your r1:

Make E the point where the radius line meets AD; so angle AOE = Q

Let a = AE: you can easily calculate length of a, since you have side r and angle Q (right triangle).

Extend OE to OF (F on BC).
You now have right triangle OFC: OF = r + x, CF = y - a
So length of OC (the longer radius) = SQRT[(r + x)^2 + (y - a)^2]

Thank you
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