Defining what tangent lines are and how they are different from other lines intersecting circles. Tangent lines are special lines that intersect a circle at exactly one point. Unlike other lines that can intersect a circle at multiple points, a tangent line touches the circle at only one point. Picture a bicycle tire spinning rapidly and imagine a line touching it without slipping off.

Tangent lines have some fascinating properties. Firstly, they are perpendicular to the radius of the circle at the point of tangency. This means that if you draw a radius from the center of the circle to the point of tangency, the tangent line will be perpendicular to that radius.

Additionally, the length from the center of the circle to the point of tangency is equal to the length of the radius. This property is particularly useful when solving problems involving tangent lines.

Remember, tangent lines are unique and have distinctive properties that make them important in geometry!