Number of Tangents from Different Point Positions

Explore how the position of a point relative to a circle determines the number of possible tangent lines

Current Case: Welcome
Point Position: Ready
Distance to Center: --
Number of Tangents: --
Tangent Length: --
Welcome! Let's explore how the position of a point determines the number of tangent lines to a circle.
Case 1: Point Inside Circle
Result: No tangents possible

When a point lies inside a circle, every line through that point will intersect the circle at two points, making all lines secants rather than tangents.

Case 2: Point On Circle
Result: Exactly one tangent

When a point lies on the circle, there is exactly one tangent line at that point, perpendicular to the radius through that point.

Case 3: Point Outside Circle
Result: Exactly two tangents

From any external point, exactly two tangent lines can be drawn to the circle, touching at two distinct points of contact.

Key Terminology

Length of Tangent

The distance from an external point to the point where the tangent touches the circle.

Point of Contact

The specific point where a tangent line touches the circle.

External Point

A point that lies outside the circle, from which two tangents can be drawn.