A point on a circle can have the following number of tangents traced to it:

No tangent can be drawn from a point that is inside the circle. When a point is on a circle, there can only be one tangent from that point. Two tangents can be drawn from a point that is outside the circle.

Consider a circle with a centre $\mathrm{O}$and a point $\mathrm{P}$on it, and draw a line  (say $\mathrm{m})$perpendicular to the radius OP.

Take any point Q on the line $\mathrm{m}$, and we can say that $O P<O Q$ because OQis the hypotenuse of the $∆OPQ$

We can say that Q is an exterior point because it lies outside the circle, and this is true for all points on line $\left(m\right)$except the point P which is on the circle.

We can say that tangent at any point of a circle is unique because the line touches the circle at a single point.

As a result, only one tangent to a circle can be drawn from a point on the same circle