If a point lies inside a circle

If a point lies on the circle

If the point lies outside the circle

If centre of the circle is not given

there cannot be a tangent to the circle through this point

there is only one tangent to the circle at this point and it is perpendicular to the radius through this point.

there will be two tangents to the circle from this point.

by taking any two non-parallel chords and then finding the point of intersection of their perpendicular bisectors.