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enter image description hereHere is an arc with known coordinates at starting & ending points.

The curve's starting & ending point coordinates are $A (0.19,0)$ and $B (0.1375,0.22)$ respectively.As curve is assumed to be a part of a circle whose center would be at $C (0,0.11)$ with radius $0.15$.

If a horizontal line (intersecting the curve) drawn at a distance $y=0.02$ ,what would be the possible method to find out the $x$ coordinate of that point of intersection?

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    $\begingroup$ Can you show some work? $\endgroup$
    – Julian Rachman
    Dec 23, 2014 at 9:59
  • $\begingroup$ It seems a data is missing. There is an infinity of arcs that goes through $2$ specific points... You need the curvature, that is the center of the arc. $\endgroup$
    – Martigan
    Dec 23, 2014 at 10:18
  • $\begingroup$ @ Julian Rachman- the curve's starting & ending point coordinates are A(0.19,0) & B(0.1375,0.22) respectively.As curve is assumed to be a part of a circle whose center would be at c(0,0.11) with radius 0.15. If a horizontal line(intersecting the curve) drawn at a distance y=0.02 ,what would be the possible method to find out the x coordinate of that point of intersection? $\endgroup$
    – user202851
    Dec 23, 2014 at 10:20

1 Answer 1

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The equation of the circle of center $C (0,0.11)$ and of radius $0.15$ is

$x^2+(y-0.11)^2=0.15^2$

The equation of the line is $y=0.02$

From there it is easy to find the intersection points.

And since you want only the point intersecting the arc, you have to see which point belongs to the arc.

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  • $\begingroup$ @Martigan- I have tried this method but when it is applied to verify the x coordinate of B, it gave wrong answer. $\endgroup$
    – user202851
    Dec 23, 2014 at 10:45
  • $\begingroup$ @user202851 The issue is that the radius you gave is clearly wrong. You can't have a center $C$ with a radius $0.15$ that goes through $A$. The distance $CA$ is greater than the radius... $\endgroup$
    – Martigan
    Dec 23, 2014 at 12:32
  • $\begingroup$ @Martigan-I got your point that the center point assumed here is wrong. Can you suggest what it should be by observing the diagram? $\endgroup$
    – user202851
    Dec 24, 2014 at 4:14
  • $\begingroup$ @user202851 Since the distance between $A$ and $B$ is also greater than $0.15$ (easy to see because $y$ coordinates of $A$ and $B$ differ by $0.22$, which is greater than $0.15$), you have to assume that the radius is wrong. Since the distances between $C$ and $A$ and $C$ and $B$ are also different, you can't take any og them as the radius... You have no way of solving this. $\endgroup$
    – Martigan
    Dec 29, 2014 at 9:40
  • $\begingroup$ Pro-tip: transform everything so the arc is on the unit circle. The math becomes easier. This will even let you find the intersection of an elliptical arc. $\endgroup$
    – Edward Falk
    Nov 18, 2015 at 20:19

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