Find the centre of a circle given two points lying on it and its radius
$$INPUT \rightarrow P_1(x_1, y_1), P_2(x_2,y_2), r$$

$$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$$
$$h=\sqrt{r^2-(\frac{d}2)^2}$$
$$\alpha=arcsin(\frac{y_1-y_2}{d})$$
$$x_c=\frac{x_1+x_2}2+h sin(\alpha)$$
$$y_c=\frac{y_1+y_2}2+h cos(\alpha)$$