Find Radius, given values of X, Y (I know it involves chord length)

[ahurst210]

Hello, in the attached picture, how would I go about finding the radius (R) in the shape, when I'm given the values of X and Y? I know it involves finding the chord length of a circle but I'm not entirely sure of how to go about it?

Any help would be greatly appreciated , thanks!

 

[stapel]

Hello, in the attached picture, how would I go about finding the radius (R) in the shape, when I'm given the values of X and Y? I know it involves finding the chord length of a circle but I'm not entirely sure of how to go about it?

What other information are you given? For instance, is the point of intersection, on the far left, between the base of the shape and the curved line, tangent to, say, the lowest point on the circle? If there is no further information, then I suspect that this question is unanswerable.... :shock:

 

[tkhunny]

Do we know that P is a piece of a Circle?

 

[mmm4444bot]

… in the attached picture, how would I go about finding the radius (R)

In the attached image, R is not a radius. It is the length of a curved line.

Please post the entire exercise, as it was given to you. Thanks! :cool:

PS: Here's a link to the forum guidelines

 

[mmm4444bot]

Maybe the diagram is mislabeled. If the curved line is circular and symbol R is actually supposed to represent the circle's radius, then you may use the following information, to find the length of the radius.

In the diagram above, S is the segment height, L is half the chord's length, and R is the circle's radius.


If you know any two of these three measurements, you can find the third.


S = R - √[R^2 - L^2]


L = √[2SR - S^2]


R = (S^2 + L^2) / (2S)

 

[ahurst210]

Sorry, Let me add a little more information about what I'm trying to do.

In the diagram that I provided, yes R is supposed to represent the unknown radius of the circle that makes up that line, not the length of the curved line.

What I'm doing is trying to come up with a formula that will calculate that changing radius if Y constantly stays the same but x changes in length. This is for a program that will create that curved side according to what value you enter in x.

for example

let's say

y will always equal 152.4
x is a changing value that you're given and are supposed to enter
and the radius (R) is what will be created off those two values

as you make x larger or smaller, essentially stretching that shape, your radius changes along with it.

The previous person that was working on this came up with a formula that supposedly does this, but I'm having trouble deciphering what he's doing.

The following is exactly what he has...

R=(152.4/2)+(X*2)*(X*2)/(8*152.4)

Again, all the information that he was given was just Y=152.4, and X.
In this scenario x=1524... if that helps.

Sorry if I'm not explaining very well. I still assume he's using chord equations because that makes the most sense but I'm totally lost on what he's got going on there.






he circle's radius, then you may use the following information, to find the length of the radius.

In the diagram above, S is the segment height, L is half the chord's length, and R is the circle's radius.


If you know any two of these three measurements, you can find the third.


S = R - √[R^2 - L^2]


L = √[2SR - S^2]


R = (S^2 + L^2) / (2S)[/QUOTE]

 

[ahurst210]

Yes, that far left side would be tangent to the lowest point of the circle!

What other information are you given? For instance, is the point of intersection, on the far left, between the base of the shape and the curved line, tangent to, say, the lowest point on the circle? If there is no further information, then I suspect that this question is unanswerable.... :shock:

 

[mmm4444bot]

The following is exactly what he has...

R=(152.4/2)+(X*2)*(X*2)/(8*152.4)

That formula for R represents:

\(\displaystyle R = \dfrac{Y}{2} + 2X \cdot \dfrac{2X}{8Y}\)

It simplifies to:

\(\displaystyle R = \dfrac{X^2 + Y^2}{2Y}\)

This is the same formula for R that I provided you earlier, where Y is the height of the circle segment and X is half the chord length. :cool:

PS: Don't interchange upper- and lower-case symbols (like x and X, or y and Y). Pick one symbol for each measurement, and then use it consistently throughout.

 

[Bob Brown MSEE]

xx+(y-r)(y-r) = rr

solve for r in terms of x and y