Get the equation of a circle when given 3 points Get the equation of a circle through the points $(1,1), (2,4), (5,3) $.
I can solve this by simply drawing it, but is there a way of solving it (easily) without having to draw?

As a programmer this was the best solution for me  as there is no division by zero:
For given (x1,y1) , (x2,y2) and (x3,y3) first form A,B,C:
$$A=x_1(y_2-y_3) - y_1(x_2-x_3)+x_2y_3 -x_3y_2$$
$$B=(x_1^2 + y_1^2)(y_3-y_2)+(x_2^2+y_2^2)(y_1-y_3)+(x_3^2+y_3^2)(y_2-y_1)$$
$$C=(x_1^2+y_1^2)(x_2-x_3)+(x_2^2+y_2^2)(x_3-x_1)+(x_3^2+y_3^2)(x_1-x_2)$$
$$D=({x_1^2}+{y_1^2})({x_3}{y_2} - {x_2}{y_3})+(x_2^2 + y_2^2)(x_1y_3-x_3y_1)+(x_3^2+y_3^2)(x_2y_1 - x_1y_2)$$
If A=0 then the points are colinear elasewhere using A,B,C you can find center and radius of circle:
$$x_c=-B/2A$$
$$y_c=-C/2A$$
$$r= \sqrt {\frac {B^2+C^2-4AD}{4A^2}}$$
Finally the formula of the circle is:
$$(x-x_c)^2+(y-y_c)^2=R^2$$
