I am trying to show that if a line given by $y = mx + b$ intersects an Elliptic Curve given by $E(\mathbb{K}): y^2 = x^3 + Ax + B$ in three points then the line is not tangent to the curve.
Given that char$(\mathbb{K}) \neq 2,3$ and $\mathbb{K}$ is algebraically closed.
Also that if they intersect in two points, the line is tangent to the curve. And if they intersect in one point, the intersection is an inflection point.
I have tried to characterize the points of intersections and compare the slope of the line and curve at those points but I'm not getting anywhere.
any help is deeply appreciated.