Four points on a plane are given which are not collinear or all on one circle. How many straight lines and circles can be drawn in the plane so that they are equidistant from all four points?
If not collinear I believe that we cannot draw any lines, as the line could only possibly be equidistant from the other 3 at any given point on the line. It may be possible to be equidistant from all 4 if and only if we are only looking at specific point on the line
Not sure how I would go about drawing the circle
Any help would be appreciated
Hint: There are only two distances from the circle'a center $O$ to $A,B,C,D$. They are $r+d$ and $r-d$. One option is that $O$ is equidistant from $A$, $B$ and $C$.