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Old 05-30-2004, 06:07 PM   #1
linuxfond
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MATH - Radius of an arc


Hello,
I gota a math puzzle:
````````d`````````
A_______|________B
````````c ````````

AB is 60, and the perpendicular cd is 12.
An arc AdB (which I can not draw here) is drawn from A to B, and it intersects cd at point d. Diameter of the arc is 40.

What is the diameter of the arc if AB is 65?
What is the diameter of the arc if cd is 15?



Thanks

Last edited by linuxfond; 05-30-2004 at 06:16 PM.
 
Old 05-30-2004, 07:52 PM   #2
andrewlkho
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Okay, I'm working on it. It must be possible, as there is only one arc that can fit in that .... (I can tell this problem will haunt me until I solve it).

Will post back the answer, and will be extremely pissed off if I can't get it - it's simple geometry.
 
Old 05-31-2004, 05:45 PM   #3
andrewlkho
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Well I hate to tell ya, but for the 60 / 12 one, I don't get an arc of diameter 40.... Are you sure that's right?
 
Old 05-31-2004, 05:46 PM   #4
linuxfond
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Sorry, my numbers may be somewhat imprecise. In fact, these numbers are almost arbitrary: they were returned by another somewhat sloppy scripting in my program, but that I will correct later.

There is just one arc that can fit in; we know neither the ratio between cd and the diameter nor the ratio between cd and AB.

On my example it may seem that cd is 1/5 of AB, but it is not.

cd can be 1mm, while AB can be 1000km, yet, there is just one arc that will fit in.

I can display the problem otherwise:

A__________B
C|...............|D

What is the value of AB and CD if the arc inscribed inside has a diameter x, where x is a known decimal?


Last edited by linuxfond; 05-31-2004 at 05:55 PM.
 
Old 05-31-2004, 05:52 PM   #5
acid_kewpie
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please do not ask homework questions on LQ.org... we're not the ones supposed to be learning stuff. and besides you'll need to be able to invent soem convincing working-out in pencil in the margin before you hand it in.... you can always tell fake workings.
 
Old 05-31-2004, 05:58 PM   #6
linuxfond
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Dear Moderator,
Indeed, I had doubts about asking this question here. I did it because I need a formula to be embedded into a PHP script, which is supposed to produce correct graphics. I run out of pencils.
 
Old 05-31-2004, 07:43 PM   #7
andrewlkho
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Well if ya still want the answer, then e-mail me. I'll attach an image showing how to do it....
 
Old 06-01-2004, 10:40 AM   #8
eric.r.turner
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Your email is disabled in Linuxquestions.org. How do we contact you?
 
Old 06-01-2004, 04:01 PM   #9
andrewlkho
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Whoops, sorry, forgot that. It's enabled now.
 
  


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