Tangent and Radius Theorem

The tangent and radius theorem states that a radius drawn to the point of tangency is perpendicular to the tangent line.

Explanation:

When a circle is drawn with a center and a point outside the circle, the line connecting the center of the circle to the point is the radius. A tangent line is a line that touches the circle at exactly one point. The tangent and radius theorem states that the radius drawn to the point of tangency is perpendicular to the tangent line. In other words, the angle between the radius and the tangent line is a right angle.

Study Guide:

Here are some key points to remember about the tangent and radius theorem:

1. A radius is a line segment from the center of a circle to any point on the circle.
2. A tangent is a line that touches the circle at exactly one point.
3. The point where the tangent touches the circle is called the point of tangency.
4. The tangent and radius theorem states that the radius to the point of tangency is perpendicular to the tangent line.
5. This means that the angle between the radius and the tangent line is a right angle.

It's important to understand and apply this theorem when solving problems involving circles and tangents. Practice drawing circles, tangents, and radii to better understand this concept.

Remember that the tangent and radius theorem is a fundamental concept in geometry and is often used in various proofs and problem-solving scenarios involving circles.

With this understanding, you can confidently apply the tangent and radius theorem to solve problems and understand the relationships between tangents, radii, and circles.

Good luck with your studies!