Theorem: The theorem states that “the tangent to the circle at any point is the perpendicular to the radius of the circle that passes through the point of contact”.
Here, O is the centre and OP XY.
i) If the point is in an interior region of the circle, any line through that point will be a secant. So, no tangent can be drawn to a circle which passes through a point that lies inside it.
AB is a secant drawn through the point S
ii) When a point of tangency lies on the circle, there is exactly one tangent to a circle that passes through it.
A tangent passing through a point lying on the circle
iii) When the point lies outside of the circle, there are accurately two tangents to a circle through it
Tangents to a circle from an external point