This question occurred to me doing this circle geometry problem, and I was wondering if anyone could clear it up. Geometrically, it seems it would make sense, provided that 2 sides are equal (equal radii), but I am still unsure.
I specifically refer to triangle ABC. Since BC=AC, is it possible that another circle can be formed about the centre C with radius AC (or BC), like this:
You can form a circle of any radius about any point.
If you used the vertex between the equal legs as the center, and a radius equal to the length of these legs, the ends of these legs would necessarily fall on the edge of said circle.
But if you pick a vertex between unequal legs, it will of course be impossible to get the end points to fall on a circle. That would be saying the circle had two different radii...
And finally, any two radii you pick (which don't fall on a straight line) can be taken as legs of another isosceles triangle when you connect their end points.