Single Varible Calc, Multiple, or neither?

[BaDaBooM]

Ok, fine... I admit it. My teacher was right. I will in fact need this "stuff" later in life. I'm talking about calculus or so I think. It has been a long time since I was in calc so I forget most of this stuff. Here is the problem:

I need to determine the size of a circle. What I have is a line segment at a shallow angle off the edge of the circle I need to find. I know the length of the line segment and the length of a line segment perpendicular to it. At the non-intersecting ends of each line segment, are two points. If you connected those two points with a straight line, it would make a right triangle. I need to connect the two points with an arch and figure out the radius of the circle that arch would make if it continued on.

So it's been forever since I did this in school but I can do the calculations myself. I just need a refresher of what equation(s) I need to use and of what each variable stands for. Thanks ahead of time.

 

[SpecialEd]

I believe if you have an inscribed right triangle in a circle, the hypotenuse is always the diameter. Anyway, I found this website which may have the formulas you are looking for

Text

 

[BrownTown]

algebra

(A^2+B^2)*Pi/4

that right?

 

[BaDaBooM]

The triangle is mostly outside the circle... I made a crappy drawing here :

Crappy drawing!

 

[BrownTown]

you sure thats possible?

 

[BaDaBooM]

No, of course not . If it is not then I guess I would want to find out what I'm missing (beside what I know I am missing) and what the parameters are around this scenario to determine the size or possible sizes of the circle.

 

[PottedMeat]

hmm maybe theres something that relates arc length to a and b. from that i guess you find the circumference then the radius?

 

[pcy]

Hi,

If the line whose length is a is a tangent to the circle, then:

r = (a*2 + b*2)/2b


If not there are an infinite number of circles (all of different sizes) which pass thriough the end point s od teh line segment.



Peter

 

[BaDaBooM]

It is not necessarily tangent. hmm.... so if I limit the intersection of a and b to being outside the circle and the circle can only intersect a and b at their end points, that would give me a finite range of possible circles (no ovals, circles only), right? If that is true, how would I find that range? This leads me to believe that I may need calculus for this.

*edit* I'm thinking now that a range may not be necessary... if I could get a minimum radius that would work. Because taking above into consideration, it could then be infinite above a certain radius, correct?

 

[pcy]

Hi,


Errrrrrrr No.


The circle intersects lines a and b (by which I take it you mean the lines whose lengths are a and b) at their end points; becase they meet the ends of the line segment at their end points and the circle, by definition, passes through the end points of the line segment.

The circle might, or might not intersect lines a and be a second time, but constraining it not to do so will still leave you with an infinite number of possible circles.

The problem is that the lines a and b tell you nothing about the circle. They tell you only the length of the original line segment - (a*2 + b*2)*0.5

You need to know the angle between the line a and the circle (i.e strictly speaking between line a and the tangent to the circle at the point where line a meets the circle) in order to define the circle. The easiest way to do that, clearly, is to define line a to be a tangent.


And No. No calculus is needed.





Peter

 

[BaDaBooM]

Thanks pcy! I get what you are saying now. I was having a mental block for some reason... In visualizing it, I was roling the line along the circle instead of changing the angle of the line from being tangent. Now, that I am properly visualizing it, I think the tangent is inherently the best solution for me.