Imagine a point outside a circle. Suppose you draw a line from the point passing through the center of the circle, the line intersects the circle at two points. The segment of the line within the area of the circle is equal to the diameter of the circle. When you keep increasing the angle of direction of the line, the points of intersections get closer and closer. The line segment within the circle changes to chords of shorter and shorter lengths from the size of the diameter. Ultimately, the intersection points on the circle coincides each other and the line just touches the circle at only one point. At this condition, the line is called as the ‘tangent’ of the circle from that point.
With further increase in angle of direction of the line will not at all intersect the circle.
In this article let us study the properties of the tangent of a circle.

We have explained in the introduction how a line from a point outside the circle could be a tangent to that circle. Now let us formally define what a tangent of a circle is. A line drawn from a point outside a circle which touches the circle just at one point is called tangent to the circle. The point of contact of the tangent and the circle is called as the ‘point of tangency’.
Tangent of a Circle
The above diagram shows a circle with center O and a tangent PA drawn from a point P outside the circle. The point A is called the point of tangency.