Circle Theorems

Tangent perpendicular to the radius at the point of contact

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\bot XY.

The number of tangents drawn from a given point

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

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