Question

In the figure, $PA$ and $PB$ are tangents to the circle drawn from an external point $P$. Also $CD$ is a tangent to the circle at $Q$.
If $PA=8cm$ and $CQ=3cm$, then $PC$ is equal to:

• A. $11cm$
• B. $5cm$
• C. $24cm$
• D. $38cm$

Answer 1

The correct option is B $5cm$

As we know that tangents drawn from any external point (here, it is P) to a circle are equal in length. So,$PA=PB$.

1) $CQ=CB=3$ cm

(Since C acts as an external point from where tangents CB & CQ are drawn to the circle, and we know that tangents drawn from any external point to a circle are equal in length, so $CQ=CB$ (similar to the way we proved $PA=PB$)

2) $PB=PA=8$ cm

Now, Since $PC+CB=PB=8$ cm

$=>$ $PC=(8-CB)cm=(8-3)cm=5$ cm.

Hence, Option B is the correct answer.