Originally Posted by

**wingless** If you want to get the equation using calculus, follow these steps:

1- Write the circles as an equation. (Like $\displaystyle (x-x_0)^2 + (y-y_0)^2 = r^2$). Then, convert them to functions of x. The thing is, one equation will give you two functions of x, each of them making top and bottom semicircles. Take the functions of top semicircles. For example,

$\displaystyle (x-x_0)^2 + (y-y_0)^2 = r^2$

$\displaystyle (y-y_0)^2 = r^2-(x-x_0)^2 $

$\displaystyle y-y_0 = |r^2-(x-x_0)^2|$

$\displaystyle y = y_0 + r^2-(x-x_0)^2$ (top semicircle), $\displaystyle y = y_0 - r^2-(x-x_0)^2$ (bottom semicircle)

...