



 
Hi Isiah, I am going to change your setup slightly. I want to find the equation of the circle and since the equation of a circle is easiest \[x^2 + y^2 = r^2 \mbox{ where $r$ is the radius,}\] when the central of the circle is at the origin I am going to move $(0, 0)$ to the centre of the circle. In my diagram $s$ is the length of the sagitta, $c$ is the length of the chord, $r$ is the unknown radius of the circle nd $C (0,0)$ is the centre of the circle. Triangle ABC is a right triangle so a use of Pythagoras Theorem will allow you to solve for $r.$ Once you have the radius of the circle you can use the equation \[y = \sqrt{r^2  x^2}\] to solve for $y$ for points at a distance $x$ from $C$ along the x axis. At each such point the height of the arc above the chord is $y  (r  s).$ Penny
 


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