Chord Length vs Chord Arc Relationship Question

[labanaul]

If I have a circle R75, what is the chord height h from the perimeter when the chord length and chord arc length is equal to 10% difference?

 

[Dr.Peterson]

The question is not quite clear. I presume R75 means the radius is 75; and I presume "chord height" means the distance from the midpoint of the chord to the midpoint of the arc. But what does "is equal to 10% difference" mean? What difference is 10% of what?

 

[pka]

If I have a circle R75, what is the chord height h from the perimeter when the chord length and chord arc length is equal to 10% difference?

Here is one reference: PAGE ONE & Another
You can see the standard terms used.

 

[labanaul]

The question is not quite clear. I presume R75 means the radius is 75; and I presume "chord height" means the distance from the midpoint of the chord to the midpoint of the arc. But what does "is equal to 10% difference" mean? What difference is 10% of what?

Length A to Length C (C being longer) = 10%

 

[Deleted member 4993]

View attachment 16904
Length A to Length C (C being longer) = 10%

Is it:

(A - C)/ A = 0.1

or

(A - C)/ C = 0.1

 

[Dr.Peterson]

If I have a circle R75, what is the chord height h from the perimeter when the chord length and chord arc length is equal to 10% difference?

View attachment 16904
Length A to Length C (C being longer) = 10%

That's funny; you said "chord height from the perimeter", which led me to assume you meant the segment height; but here you show the "height" from the center. Which do you really mean?

And you haven't explained the percentage. First, it is obvious that A is longer than C, contrary to what you said! Then, are you saying that A is 10% of C, or that C is 10% longer than A?

In any case, I expect this to require a numerical solution, as the equation involved will be transcendental. I presume that is all you need. (But it would be helpful to know something about why you want this.)

 

[labanaul]

(A - C)/ C = 0.1

 

[Dr.Peterson]

Please show whatever work you have done. You were given some references in post #3 that should help you write an equation representing your condition that the arc length s is 10% greater than the chord c. It's probably easiest to express this in terms of the angle you called x (and they call theta), by writing s and c in terms of theta. To solve the equation, you'll need some technology, such as a graphing calculator or online equivalent, or perhaps Excel. Let us know what you want to use, and we can help you use it.