Tangents to Circles 

Geometrically a line which intersects a circle exactly once; in calculus, a line which touches a curve at 1 point and whose slope is equal to that of the curve at that point. Particularly useful as approximations of curves in immediate vicinity of the point of tangency, tangent lines are the basis of several estimation techniques, including linear approximation. The numerical value of slope of the tangent line to the graph of a function at any point equals that of the function's derivative at that particular point. A line sharing a common point with the curve or surface and being the closest linear approximation of the curve or surface at that point.

 A tangent line t to the circle C intersects the circle at a single point T. For comparison, secant lines intersect a circle at 2 points, whereas another line may not intersect a circle at all. This property of tangent lines is preserved under many geometrical transformations, such as scaling, translations, rotation, inversions, and map projections. The tangent line through a point P on the circle is perpendicular to diameter passing through P. Tangent to the circle is a line which intersects the circle in exactly 1 point.

At a point of a circle there is one only tangent.

The tangent at any point of the circle is perpendicular to the radius through the point touching.

Lengths of tangents drawn from the external point to the circle are equal.

• The centre of circle lies on the bisector of angle between the 2 tangents. Tangent to a circle is the line that intersects the circle in one point exactly. A tangent touches a circle in exactly one place
• The tangent intersects the circle's radius at a 90° angle

As a tangent only touches the circle at exactly 1point, that point should be perpendicular to a radius. To test out the interconnected relationship of these 2 defining traits of a tangent. It's only when the line is tangent to the circle that the radius will touch that line at exactly 1 point and at this point the line segment or 'tangent' should intersect with the radius at a 90° angle.
The point where tangent and circle intersect is called as tangent of a circle. A tangent to a circle is a straight line, in the plane of circle, which touches the circle at only 1 point. The point is known as point of tangency or the point of contact.

The radius that passes through the point of contact is perpendicular to the tangent.

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