The word "tangent" has a couple of meanings depending on the context:
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In Geometry: A tangent is a straight line that touches a curve at a single point without crossing it. For example, in the case of a circle, a tangent touches the circle at exactly one point.
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In General Usage: The term "tangent" can refer to a digression or a change in thought or discussion. When someone goes off on a tangent, they may start talking about something that is only loosely related to the main topic.
The Latin root "tactus" relates to touch, which is relevant in the geometric sense of touching a curve without intersecting it.