Question

The length of a tangent of a circle of radius $3 \,\text{cm}$ drawn from a point at a distance of $5 \,\text{cm}$ from the centre will be:
 

• A. $3 \,\text{cm}$
• B. $4 \,\text{cm}$
• C. $5 \,\text{cm}$
• D. $6 \,\text{cm}$

Hint:

For tangent length from an external point, always apply $PT = \sqrt{OP^2 - r^2}$. This avoids lengthy geometric constructions.

Answer 1

The Correct Option is B

Step 1: Recall tangent-radius property
If $OP$ is the distance from the centre $O$ to the external point $P$, $r$ is the radius, and $PT$ is the tangent length, then by Pythagoras theorem in $\triangle OPT$: \[ PT^2 = OP^2 - r^2 \]

Step 2: Substitute values
Here, $OP = 5 \,\text{cm}$ and $r = 3 \,\text{cm}$.
\[ PT^2 = 5^2 - 3^2 = 25 - 9 = 16 \] \[ PT = \sqrt{16} = 4 \,\text{cm} \]

Step 3: Conclusion
The length of the tangent is $4 \,\text{cm}$.
The correct answer is option (B).