I am having some issues on how to find the coordinate on a circle.
For example I have the below part of a circle where I know :
1) the chord d
2) the height h
Based on those 2 I can calculate the radius of the circle with this formula:
$$R=(d^2+4h^2)/(8h)$$
Now I want given any X coordinate to calculate the Y coordinate so that I get the point on the circles circumference
For example if c=d/2 what is the height h' ?
Any idea how may I do this, any idea ?
Thanks in advance.
Also I know that I have some questions closed but i wasn't able to answer them, so I'm sorry.
Best Answer
The equation of the circle in your setup is
$$\left(x-\frac d2\right)^2+(y+R-h)^2=R^2$$
So, given $x=c$, the corresponding $h’=y$ is
$$h’= \sqrt{ R^2-\left(c-\frac d2\right)^2}-(R-h)$$
where,
$$R=\frac{d^2+4h^2}{8h}$$