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yes, the slope of the line is the tangent of the angle
The diameter is the distance across the circle. So if you split the circle in half by drawing a line through it, the diameter would be the length of that line.
Tangent line is a graph. This graph is to gather data.
The tangent line is the instantaneous rate of change at a point on a curve. The secant line crosses a curve twice at points A and B, representing the average rate of change between those two points.
A tangent line is a line that is parallel to and intersecting a point on a curve, where the limit of the distance between two points on that curve (one of them being the point in question) and those two points also being on that line approaches zero. Since a straight line has only one slope, at all points on the line, then there can only be one tangent line to a straight line, and the tangent line is the same line as the straight line.