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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 P on a circle with centre O is always less than OP.
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Answer

True.
PT and OT are the tangent and radius respectively at contact point T. So, $\angle\text{OTP}=90^\circ$ $\Rightarrow\ \triangle\text{OPT}$ is right angled triangle. Again, in $\triangle\text{OPT}$ $\because\ \angle\text{T}>\angle\text{O}$ $\therefore\ \text{OP}>\text{PT}$ [Side opposite to greater angle is larger] Hence, the given statement is true.

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