Point of Tangency
Point at which a tangent line intersects the circle to which it is tangent
A point of tangency is a point where a straight line or curve touches and intersects another curve or surface, and where the tangent line to the curve is perpendicular to the radius line that connects the center of the curve to the point of contact. In simpler terms, it is the point where a tangent to a curve or a circle touches it, and it lies on the curve.
The point of tangency is significant in calculus and geometry, as it provides a key point of reference for studying the properties of curves and circles. For example, a circle can be defined as a set of points that are equidistant from its center, and the point of tangency is the point where a tangent line is just touching the circle at a single point.
In practical applications, the point of tangency is frequently used in engineering, as well as in the construction of machines and structures such as bridges, where curves and circles play a significant role. By understanding the point of tangency, engineers can determine the optimum point of contact between curved surfaces, which can help to minimize wear and tear or improve the efficiency of the machines or structures.
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