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Although normally it is the line that is considered to be tangent to an arc, an arc can be tangent to infinitely many lines and so the answer to the question is: in infinitely many ways.
Secants are chords that go through a circle ONCE! Tangents are rays or segments with one point touching the border of a circle and nothing else.
You can have a tangent line for every point on a circle, so the answer is theoretically infinite.
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Generally, no. All circles contain an infinite number of chords, as a chord can be created between any two points on the circle. With an infinite number of points on the circle we can create an infinite number of chords.