Yes. Both are defined on all points other than odd multiples of 90 degrees.
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Neither secant nor tangent pass through the center of a circle. A secant passes through one point on the circle and the tangent passes through two points on a circle.
The tangent secant angle is the angle between the tangent to a circle and the secant, when the latter is extended.
A secant line touches a circle at two points. On the other hand a tangent line meets a circle at one point.
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.
yes.