Question

In fig., $PA$ and $PB$ are two tangents drawn from an external point $P$ to a circle with centre C and radius $4cm$. If $PA$ $\perp$ PB, then the length of each tangent is:

• A. $3cm$
• B. $4cm$
• C. $5cm$
• D. $6cm$

Answer 1

Answer: (B)

$4cm$

Given that $PA$ and $PB$ are two tangent drawn from an external point $P$.

And a circle with center $C$ and radius $4$ cm and $PA\perp PB$

Join center $C$ with $A$ and $B$

Given $PA$ and $PB$ are tangent of circle.

Then $PA\perp CA$ and $PB\perp CB$

Therefore, $\angle CAP={90}^0$ and $\angle CBP={90}^0$

But given, $\angle APB={90}^0$

Therefore, $\angle CBA={90}^0$

Therefore, quadrilateral $ABCD$ has all angles equal i.e. ${90}^0$

and adjacent sides equal.

Hence, it is a square.

Therefore, length of each tangent will be $4cm$