Tangent

Definition

A tangent is a line that touches a curve at exactly one point, without crossing or intersecting it. It is perpendicular to the radius of the circle at the point of tangency, and it provides important information about the properties and behavior of circles and irregular figures.

5 Must Know Facts For Your Next Test

1. The tangent line is always perpendicular to the radius of the circle at the point of tangency.
2. The length of the tangent segment from the point of tangency to the point where it intersects the circle's center is equal to the radius of the circle.
3. Tangent lines can be used to find the measure of angles and arcs within a circle.
4. Tangent lines are important in solving problems involving the relationships between circles and irregular figures.
5. The properties of tangent lines are crucial in understanding and applying concepts related to circles and irregular figures in geometry.

Review Questions

• Explain the relationship between a tangent line and the radius of a circle at the point of tangency.
  • The tangent line is always perpendicular to the radius of the circle at the point of tangency. This means that the tangent line and the radius form a 90-degree angle at the point where the tangent line touches the circle. This perpendicular relationship is a fundamental property of tangent lines and is important in understanding the behavior and characteristics of circles.
• Describe how the length of the tangent segment from the point of tangency to the point where it intersects the circle's center is related to the radius of the circle.
  • The length of the tangent segment from the point of tangency to the point where it intersects the circle's center is equal to the radius of the circle. This is because the tangent line is perpendicular to the radius at the point of tangency, and the distance between the point of tangency and the center of the circle is the radius. This relationship is crucial in solving problems involving circles and their properties.
• Analyze the importance of understanding tangent lines in the context of solving geometry applications involving circles and irregular figures.
  • Tangent lines play a vital role in solving geometry applications involving circles and irregular figures. The properties of tangent lines, such as their perpendicular relationship with the radius and the equality of the tangent segment length to the radius, provide valuable information that can be used to determine the measures of angles, arcs, and other geometric features within these shapes. By understanding the characteristics of tangent lines, students can more effectively apply geometric principles to solve a wide range of problems related to circles and irregular figures.

Related terms

Radius:

The distance from the center of a circle to its circumference, forming a straight line perpendicular to the tangent.

Secant: A line that intersects a circle at two points, cutting the circle into two parts.

Chord:

A line segment that connects two points on the circumference of a circle, forming a straight line within the circle.