Easy geometry problem, please give me a hint....

AI Thread Summary
The discussion revolves around finding the distance between a chord and the arc of a circle, with the user struggling to formulate the correct equations. They initially used the Pythagorean Theorem to calculate the height of the segment but found it inadequate for their needs. Clarifications were sought regarding the specific points and segments involved, as well as the derivation of relevant equations. Participants suggested visualizing the problem by rotating the diagram and writing down the equations for both the chord and the circle. The conversation highlights the importance of understanding the underlying concepts behind the equations used in geometry.
manareus
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Homework Statement
I'm struggling to find an equation to find the distance between two points from the segment to the arc of the circle.
Relevant Equations
I'm thinking of just using Pythagorean Theorem, but it doesn't work for the segment of a circle. Circle equations.
WhatsApp Image 2021-10-11 at 18.57.24.jpeg

I have calculated the height of the segment using the Pythagorean Theorem and that's currently where I am right now. I don't seem to find any equations that can help me. Though I might be not trying hard enough or using the wrong words because I'm not really fluent in mathematical terms as you can observe from the details that I provided.

EDIT: I might be in the wrong topics, but whatever.
 
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\sqrt{50^2-x^2}-10where x is distance from c line.
 
anuttarasammyak said:
\sqrt{50^2-x^2}-10where x is distance from c line.
Kindly explain where the equation come from?
 
anuttarasammyak said:
The equation of circle ref. https://en.m.wikipedia.org/wiki/Circle
anuttarasammyak said:
\sqrt{50^2-x^2}-10where x is distance from c line.
What did you mean by the "distance from c line" sorry? From what point?
 
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Edit. Not -10 but -40. Say x=0how much is it and where is it ?
 
manareus said:
I'm struggling to find an equation to find the distance between two points from the segment to the arc of the circle.
It's not clear to me what you're trying to find. Which two points on the line segment?

Also, a segment of a circle is a portion of the circle subtended by two radii, sort of like a piece of pie.
 
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anuttarasammyak said:
Edit. Not -10 but -40. Say x=0how much is it and where is it ?
It should be 10 and it's the sagitta, am I correct?

But I'm still not sure how can you come up with that equation though. Yes it's the equation of a circle but, if I'm wording this correctly, where did you derived this equation from?

Is it from C = πd? Or A = πr^2?

Or even r^2 = x^2 + y^2? Please guide me through it. I don't like not knowing the aspect of "why" from an equation.
 
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Mark44 said:
It's not clear to me what you're trying to find. Which two points on the line segment?

Also, a segment of a circle is a portion of the circle subtended by two radii, sort of like a piece of pie.
I'm trying to find the distance between the chord to the arc of the circle, see question mark I put on the picture I shared. Sorry if I make you confused.
 
  • #10
manareus said:
I'm trying to find the distance between the chord to the arc of the circle, see question mark I put on the picture I shared. Sorry if I make you confused.
That distance varies depending on the point of the chord you choose. Are you trying to find the distance at points 6 units apart on the chord?

I would rotate your diagram anticlockwise and write down the equation of the chord and the circle. The distance is simply the difference in y-coordinates for a given x-coordinate.
 
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  • #11
manareus said:
It should be 10 and it's the sagitta, am I correct?
So you see x as
21101221643.jpg
 
  • #12
PeroK said:
I would rotate your diagram anticlockwise and write down the equation of the chord and the circle. The distance is simply the difference in y-coordinates for a given x-coordinate.

2110121652.jpg
@manareus Do you write down equations of this upper half circle and the red horizontal line ?
 
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  • #13

PeroK said:
That distance varies depending on the point of the chord you choose. Are you trying to find the distance at points 6 units apart on the chord?

I would rotate your diagram anticlockwise and write down the equation of the chord and the circle. The distance is simply the difference in y-coordinates for a given x-coordinate.
Interesting, though I cannot admit that I am able to visualize it.
anuttarasammyak said:
View attachment 290568@manareus Do you write down equations of this upper half circle and the red horizontal line ?
Hmm I don't know actually my Professor doesn't teach me any chord equations. Probably only 1, where if one bowstring is the diameter and the other bowstring cuts perpendicularly, it will cut into two equal lengths.

Regarding the equation for a circle you mean the area or the circumference? Or the x and y one?
 
  • #14
manareus said:
Or even r^2 = x^2 + y^2?
Yes, that's it.
 
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  • #15
manareus said:
Interesting, though I cannot admit that I am able to visualize it.
See post #12.

manareus said:
Hmm I don't know actually my Professor doesn't teach me any chord equations.
In post #12 the chord is a horizontal line. You shouldn't need a professor to tell you the equation of one of those!
 
  • #16
anuttarasammyak said:
Yes, that's it.
PeroK said:
See post #12.In post #12 the chord is a horizontal line. You shouldn't need a professor to tell you the equation of one of those!
Ah okay thank you for your help!
 
  • #17
manareus said:
Homework Statement:: I'm struggling to find an equation to find the distance between two points from the segment to the arc of the circle.
Relevant Equations:: I'm thinking of just using Pythagorean Theorem, but it doesn't work for the segment of a circle. Circle equations.

View attachment 290504
I have calculated the height of the segment using the Pythagorean Theorem and that's currently where I am right now. I don't seem to find any equations that can help me. Though I might be not trying hard enough or using the wrong words because I'm not really fluent in mathematical terms as you can observe from the details that I provided.

EDIT: I might be in the wrong topics, but whatever.
Could you please indicate just what segments you're referring to here? Maybe mark them in red or other color?
 
  • #18
WWGD said:
Could you please indicate just what segments you're referring to here? Maybe mark them in red or other color?
@WWGD see the figure in the OP, there is a question mark "?" with arrows pointing to the line segments.
 
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