How many tangents can a circle have?
Answer
A circle can have infinitely many tangents, since a tangent can be drawn at each of its infinitely many points.
The working
Key result
There are infinitely many tangents to a circle because the circle has infinitely many points, and exactly one tangent touches it at each point.
Tangent at a point
At any single point on the circle, one and only one tangent line can be drawn. This tangent is perpendicular to the radius at that point.
From an external point
From a point outside the circle, exactly two tangents can be drawn, and their lengths are equal.
Point positions
From a point inside the circle no tangent exists, from a point on the circle exactly one exists, and from an external point exactly two exist.
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