Problem Detail: We have been given 2 points on a circle and its radius. Now I want to find out the centre point of such a circle. How can I code this efficiently without solving the quadratic equations?
Asked By : Nikunj Banka
Answered By : Yasser Zamani
$$INPUT rightarrow P_1(x_1, y_1), P_2(x_2,y_2), r$$ 
$$d=sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$$ $$h=sqrt{r^2-(frac{d}2)^2}$$ $$alpha=arcsin(frac{y_1-y_2}{d})$$ $$x_c=frac{x_1+x_2}2+h sin(alpha)$$ $$y_c=frac{y_1+y_2}2+h cos(alpha)$$
$$d=sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$$ $$h=sqrt{r^2-(frac{d}2)^2}$$ $$alpha=arcsin(frac{y_1-y_2}{d})$$ $$x_c=frac{x_1+x_2}2+h sin(alpha)$$ $$y_c=frac{y_1+y_2}2+h cos(alpha)$$ Best Answer from StackOverflow
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