Question

Chords $AB$ and $CD$ of a circle meet inside the circle at $P$. If $PA=4$ cm, $AB=7$ cm and $PD=6$ cm, then length of $CD$ is

• A. $8$ cm
• B. $6$ cm
• C. $2$ cm
• D. None of these

Answer 1

The correct option is A $8$ cm

We know that if two chords intersect inside a circle then the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord.

In the figure, $AB$ and $CD$ are two chords which intersect at $P$.

Given, $PA=4$ cm, $AB=7$ cm and $PD=6$ cm
Using the above statement, we can say that,

$PA\times PB=PC\times PD$

$\Rightarrow 4\times (7-4)=6\times PC$

$\Rightarrow PC=2$ cm

$\Rightarrow CD=PC+PD$

$=2+6=8$ cm

Hence, option A is the correct answer.

$\text{Point to Remember}$: If two chords intersect inside a circle, then the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord.