Intersection of three circles each with the same unknown radius I'm kind of struggling with this one;

You are given points $A(100, 42)$, $B(33,74)$ and $C(-26,6)$. Point $D$ has unknown coordinates but the distance from $D$ to $A$ is the same as that from $D$ to $B$ and that from $D$ to $C$. Determine the coordinates of $C$.

At first, I thought it would just be calculating the intersections of the three circles you can create, all three with $r = d(A,C)$, but it didn't work out too well.
Can anybody please help?

Assuming that you mean that is $D$ instead of $C$ the point whose coordinates are to be determined, note that $D$ is the circumcenter of the triangle $ABC$.
There are two basic ways to find it.
(1):
Find the equations of two of the bisectors of the sides of the triangle, and find their intersection. This is $D$.
(2):
Consider a circle $x^2+y^2+ax+by+c=0$. Substitute the coordinates of $A$, $B$ and $C$ in this equation to obtain a $3\times3$ linear system on the unknowns $a$, $b$ and $c$. Solve it. $D$ is the center of this circle.
Remark: The coordinates of $A$, $B$ and $C$ seem big. If you don't have to make the calculations by hand, you should use software. Geogebra is great for this.
