How to find the curvature of a curve from 3 points?

Question

Mathematics

Good evening. Faced a problem.
It is necessary to find the curvature of the curve from the crest points.
Tried through the radius of the circumscribed circle. He built a triangle, then calculated. But he considers correctly only if one side passes through the center of the circle.
Then I tried to deduce the equation from the system of equations of the circle through maple.
R^2 = (x1 - cx)^2 + (y1 - cy)^2
R^2 = (x2 - cx)^2 + (y2 - cy)^2
R^2 = (x3 - cx)^2 + (y3 - cy)^2
But Maple didn't give a working equation. Google didn't help. Please help.

Answer 1

What is meant by curvature?
In general, if for Google, then something like "approximation [by circles | polynomials | logarithmic | exponential]"

Answer 2

A three-point curve isn't a Bézier curve, is it?

Answer 3

your formulas