# A geometry question

Discussion in 'Off Topic [BG]' started by Hambone, Feb 11, 2005.

1. ### Hambone

Mar 18, 2000
Atlanta/Loganville
I've been trying to find the answer to this but haven't come up with it and I'm almost positive it is out there. So, I come to harvest the motliest crue of minds ever assembled - TB!

Here's my question. From the diagram below - if the length of the cord AB is known and the "height" of the arc - shown as CD is known, is there a formula to calculate the diameter or radius of the circle they inhabit?

And can we get this done without pulling out the sine tables?

2. ### bassteban

Aug 12, 2004
Northern California
If you draw a square the length/width of AB, wouldn't the diagonal(AA or BB) measurement equal the diameter?

3. ### bassteban

Aug 12, 2004
Northern California
Looking again, I realize I'm totally guessing based on the approximate size & proportions of your diagram. Is it to scale?

Sep 19, 2001
Pacific Northwest USA
If:
AB= 4.75
CD= 1.125

Diameter of the circle is 6.625.

(I held a ruler up to my monitor... )

5. ### dave_clark69Guest

Jan 17, 2003
Would you be able to give us the lengths of the sides, as in AB=5DC etc?

Sep 19, 2001
Pacific Northwest USA
But seriously folks, I'm curious on this too.

7. ### Johnny FilaFormerly "The Crusader"

Nov 21, 2004
Elmont, NY (near NYC)
Is this a real life question or a book question? If its a real life question it will be easier to answer, but maybe this will help.

The angle of the arc from A-B in degrees X (3.14x180) X CD should work, but you need the arc angle. If it's a real life problem you can probably figure it.

8. ### Nigel Tufnel

Dec 8, 2004
This is very possible, but i'm not sure if you can do it without trig. Calculate angle ADB by using 2*ArcTan(AC/CD). Draw two lines from the center to A and B. Lets call the center O. The exterior angle AOB is twice angle ADB. Then we know that the interior angle AOB is 360-ADB*2. Angle AOD is then 180-ADB. We can then solve for R in Sin(180-ADB)=AC/R where R is the radius. Multiply by 2 and you're done.

9. ### Eric Cameron

Or do like bimplizkit did and hold a ruler up to it.

Why is that never an option in math books? I ALWAYS have a tape measure on me. It's on my key chain. Why would I ever need to use this?

Oh, and to make this post even more useless, this is post #6000 for me. Since I have been here 5 years on March 25, that give me something like 3.5 posts a day. That's just sad.

Rock on
Eric

10. ### craigbG&L churnmeisterSupporting Member

Continue the lines to the center of the circle. You now have a bigger right triangle with sides equal to:

r (the longest side)
A to C (lets call this AC)
r minus C to D (lets call this r - CD)

IIRC (geometry/trigonometry was a long, long time ago) the square of the two short sides of a right triangle equals the square of the long side.

so r squared = AC squared + (r - CD) squared

do some algebra and we end up with:

r = (AC squared plus CD squared) / 2CD

or I might be completely wrong, I don't do more than addition or subtraction these days . . .

11. ### Nigel Tufnel

Dec 8, 2004
Both of our methods come out with the same answer, so that means they must be right Yours is way cleaner than mine. And bimplizkit, you might want to think about aquiring a new ruler. Going by your measurments for AB and CD, your diameter is half an inch off

Sep 19, 2001
Pacific Northwest USA

13. ### Johnny FilaFormerly "The Crusader"

Nov 21, 2004
Elmont, NY (near NYC)
I quit! I'm gonna go play bass

14. ### Mike MoneyBanned

Mar 18, 2003
Bakersfield California
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Area of a sector, right?

I have a paper with all the geometry formulas. Its out in my car. No, i will not go get it.

15. ### Bassic83

Jul 26, 2004
Texas, USSA
This is a question to find the radius of a neck you like, isn't it?

16. ### Mike MoneyBanned

Mar 18, 2003
Bakersfield California
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Fine... I'll go pooh, and then get the paper... brb

17. ### Mike MoneyBanned

Mar 18, 2003
Bakersfield California
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It was alive.

Now, area of a sector....

ah ha...

Arc Degrees/360 x PiR^2

EDIT:

That is arc degrees divided by 360 (hit enter on calculator now) times Pi times radius squared

18. ### Mike MoneyBanned

Mar 18, 2003
Bakersfield California
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Upon further reading, i do not believe that is what you wanted.

19. ### PlayTheBassaka Mac DaddySupporting Member

Dec 7, 2004
Carmichael, CA
+1. Well, not [(AC^2 + CD^2)/2CD]+1, but you know what I mean...

I needed some algebra to wake up, and craigb did indeed nail the correct answer to the problem.

20. ### Jure the second

May 10, 2000
Slovenia, Europe
Here's my solution. Haven't checked it with numbers, though.

Jure

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