find the center of the circle that circumscribes triangle ABC.
1. A (0,0),B (6,4),C (6,0)
2. A (-3,11),B (9,11),C (-3,21)
just set up and solve the three simultaneous equations.
you know that the equation of a circle is: $\displaystyle (x - a)^2 + (y - b)^2 = r^2$ where $\displaystyle (a,b)$ is the center.
take $\displaystyle (x,y)$ to be $\displaystyle (0,0),~(6,4)$ and $\displaystyle (6,0)$ respectively, you get:
$\displaystyle (0 - a)^2 + (0 - b)^2 = r^2$ .................................(1)
$\displaystyle (6 - a)^2 + (4 - b)^2 = r^2$ .................................(2)
$\displaystyle (6 - a)^2 + (0 - b)^2 = r^2$ .................................(3)
now solve this system for $\displaystyle a$ and $\displaystyle b$ only
the second problem is done similarly