UPSKILL MATH PLUS

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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.