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Circles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsCircles1 Mark
Question
Write ‘True’ or ‘False’ and justify your answer.
The length of tangent from an external point on a circle is always greater than the radius of the circle.
✓

Answer

False.
Consider any point P external to a circle away from O . Now, draw tangent PA on the circle. Clearly, $PA > r [\because P$ is external to circle and $P$ is at sufficient distance] Now, again consider any point $P_1$ on the tangent $A P$ very near to contact point $A$ of tangent $P A, P_1 A<A O$ So, it is clear that the length of the tangent $P A$ and $P_1 A$ are greater and smaller respectively than radius OA. Hence, the length of the tangent from an external point of a circle may or may not be greater than the radius of the circle. Hence, the given statment is false.

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