Tangent

In geometry, the tangent of a circle is a straight line that just touches the circle at one point, called the point of tangency. The tangent line is perpendicular to the radius of the circle at the point of tangency.

Important Concepts:

• Point of Tangency: The point where the tangent line touches the circle.
• Tangent Line: A straight line that touches the circle at a single point.
• Perpendicular: The tangent line is always perpendicular to the radius of the circle at the point of tangency.

Formulas and Relationships:

The tangent of a circle can be represented by the following formula:

Tangent = Opposite/Adjacent

Study Guide:

When studying the concept of tangent, it's important to understand the relationship between the tangent line and the circle. Practice drawing circles and identifying the tangent lines. Also, work on problems that involve finding the length of the tangent line and its relationship to the circle's radius. Additionally, practice using the tangent formula to solve for unknown values.

Here are some practice problems to help solidify your understanding:

1. Given a circle with radius 5 cm, find the length of the tangent line from a point 8 cm away from the center of the circle.
2. If the length of the tangent line to a circle is 12 cm and the distance from the center of the circle to the point of tangency is 13 cm, find the radius of the circle.

Work through these problems and review the concepts to ensure a strong understanding of tangents in geometry.