Question

$AB$ and $CD$ are two chords of a circle which intersect each other internally at $P$. If $CP=4$ cm, $AP=8$ cm, $PB=2$ cm, then find $PD$.

Answer 1

Given, $CP=4$ cm, $AP=8$ cm and $PB=2$ cm.

Let $PD=x$
We have $AP\times PB=CP\times PD$
$\Rightarrow 8\times 2=4\times x$
$\Rightarrow 16=4x$

$\Rightarrow x=4$

Thus, $PD=4$ cm