Tangent to a Circle

A tangent to a circle is a line that intersects the circle at exactly one point. This means that the line touches the circle at only one point and does not pass through the circle.

Explanation:

To understand why a tangent to a circle intersects the circle at exactly one point, we need to consider the properties of a tangent line and the definition of a circle.

Definition of a Circle:

A circle is a set of points in a plane that are equidistant from a fixed point called the center of the circle. The distance from the center to any point on the circle is called the radius of the circle.

Properties of a Tangent Line:

1. A tangent line is perpendicular to the radius of the circle at the point of tangency. This means that the line forms a right angle with the radius.

2. A tangent line intersects the circle at exactly one point. This is because if the line were to intersect the circle at two points, it would violate the definition of a circle, which states that all points on the circle are equidistant from the center.

Visual Representation:

To visualize this, imagine a circle with a center point and a radius drawn. Now, draw a line that is perpendicular to the radius and touches the circle at only one point. This line represents a tangent to the circle.

Conclusion:

In conclusion, a tangent to a circle intersects the circle at exactly one point. This is due to the properties of a tangent line and the definition of a circle. The concept of tangents to circles is important in geometry and has various applications in fields such as physics and engineering.