Final answer:Tangents are lines that touch a circle at exactly one point, known as the point of tangency. Tangents are heavily used in geometry as well as trigonometry, and are vital in the understanding of circular motion. The angle formed between the radius of a circle and a tangent at their point of contact is always 90 degrees.Explanation:The given question is related to circles and tangent lines. In mathematics, a tangent of a circle is a line that touches the circle at exactly one point. This point is called the point of tangency. The concept of a tangent is primarily used in geometry. After understanding the definition and essentials of a tangent, we can further explore the properties and theorems related to tangents.The relationship between a circle and a tangent can also be studied under trigonometry, as thetangentfunction (often abbreviated as 'tan') is one of the primary functions in trigonometry. Furthermore, this relationship is predominant in the study of circular motion where linear acceleration or thetangential accelerationincreases as the magnitude of the velocity changes. Here, the acceleration is often tangent to the motion.Another way to look at tangents is through the lens of the angle they create with the radius of the circle at the point of contact. Consider a circle with center O and a line L touching the circle at point P. Then, the line segment OP is the radius and line L is the tangent to the circle at P. By theorems of geometry, the radius and the tangent are perpendicular to each other, meaning they form a 90 degree angle.Learn more about Tangent Lines here:brainly.com/question/34923926#SPJ11...

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