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Let us analyse the number of tangents drawn from a point on a circle in this article.
Case 1:
Consider a point \(O\) inside the circle.
Try to draw tangents to the circle through the point \(O\).
It is impossible to draw a tangent from a point inside the circle as every line intersects the circle at two points.
Therefore, no tangent can be drawn from an interior point of the circle.
Case 2:
Consider a point \(P\) on the circle.
Try to draw tangents to the circle through the point \(P\).
It is possible to draw only one such tangent passing through the point \(P\) on the circle.
Therefore, only one tangent can be drawn at any point on a circle.
Case 3:
Consider a point \(P\) outside the circle.
Try to draw tangents to the circle through the point \(P\).
It is possible to draw exactly two tangents passing through the point \(P\) outside the circle.
Therefore, two tangents can be drawn from any exterior point of a circle.
The length of the segment of the tangent from the external point \(P\) and the point of contact \(A\) or \(B\) with the circle is called the length of the tangent from the point \(P\) to the circle.
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