Some of the important theorems based on tangent properties of a circle are given below with their respective examples.

Theorem 1

The tangent to the circle is perpendicular to the radius of the circle at the point of contact.

Theorem 2

If two tangents are drawn from an external point of the circle, then they are of equal lengths.

Theorem 3

If from a point outside a circle, a secant and a tangent are drawn, then the tangent is the mean proportional between the secant and its external segment.