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In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs.
A tangent of a circle is a straight line that touches the circle at only one point. Let’s explore the definition, properties, theorems, and examples in detail.
A tangent to a circle is a line which intersects the circle in exactly one point.
A line that touches the circle at a single point is known as a tangent to a circle. The point where tangent meets the circle is called point of tangency. The tangent is perpendicular to the radius of the circle, with which it intersects. Tangent can be considered for any curved shapes.
The tangent of a circle is defined as a straight line that touches the circle at a single point. The point where the tangent touches the circle is called the ‘point of tangency’ or the ‘point of contact’.
Tangent lines to a circle. This example will illustrate how to find the tangent lines to a given circle which pass through a given point. Suppose our circle has center (0; 0) and radius 2, and we are interested in tangent lines to the circle that pass through (5; 3).
As the secant line moves away from the center of the circle, the two points where it cuts the circle eventually merge into one and the line is then the tangent to the circle. As can be seen in the figure above, the tangent line is always at right angles to the radius at the point of contact.