Point of tangency
When a line intersects a circle in exactly one point
In geometry, a point of tangency is a point where a tangent line touches a curve or a surface. The tangent line is a line that touches the curve at just one point and has the same slope as the curve at that point. At the point of tangency, the tangent line and the curve share the same point, known as the point of intersection.
For example, a circle is a curved shape with a constant radius, and if we draw a line that touches the circle at just one point, that line is called a tangent line. The point where the tangent line touches the circle is called the point of tangency.
The point of tangency is important because it helps us to calculate the slope and other properties of the curve at that point. It also helps us to understand the behavior of the curve near that point. Furthermore, the point of tangency is crucial in optimization problems, where we want to find the maximum or minimum value of a function at a particular point.
In summary, the point of tangency is a fundamental concept in geometry that plays a vital role in analyzing curves and surfaces. It marks the point where a tangent line touches a curve or a surface, and it is essential in calculating various properties of the curve at that point.
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