Tangent to a circle


Tangent to a circle: A tangent to a circle is a line that intersects the circle at only one point and there is only one tangent at a point of the circle. The tangent to a circle is a special type of secant, when the two end points of its corresponding chord coincide and the common point of the tangent and the circle is called the point of contact.

Number of tangents from a point on a circle:

The number of tangents that can be drawn from a point to the circle, depends on the position of the point relative to the circle.

The following cases show the position of points and number of tangents that can be drawn to the circle from that point.

Case – I

When the point lies on the circle, then only one tangent can be drawn from this point to the circle.

Case – II

When the point lies outside the circle then number of tangents that can be drawn from this point to the circle is two.

Case – III

When the point lies inside the circle, then any line passing through it, will intersect the circle in two points. Hence this line cannot be a tangent. Thus, no tangent can be drawn from a point inside the circle.

Properties of tangent:

(a) A tangent to a circle is perpendicular to the radius, drawn from the point of contact.

(b) From a point, lying outside a circle, two tangents can be drawn to the circle; which are equal in length.

Here, AB = AC