Given 3 points and there distances from eachother find a fourth point equidistant to the 3.

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This question can also be asked: given a triangle, and its dimensions, whose vertices lie on the edge of a circle find the radius of the circle.

I am not actually sure if there is enough information to solve this problem (I conjured it myself) but I have the strongest intuition that there is. It just makes perfect sense visually in my head that this should be answerable, but I have failed to formalize this intuition. Thanks in advance!

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According to this Wikipedia article, the diameter of the circumscribed circle of a triangle can be found in terms of the length of its three sides, $a,b,c$ :

$$\frac{abc}{2\sqrt{s(s-a)(s-b)(s-c)}}$$

where $$s = \frac{a + b + c}{2}$$.