Question

Let $AB$ and $CD$ are two parallel chords of circle whose radius is $5$ units . If $P$ and $Q$ are mid points of $AB$ and $CD$ respectively such that $PA.PB=9,QC.QD=16,$ then distance between $AB$ and $CD$ is

• A. $5$
• B. $25$
• C. $7$
• D. $11$

Answer 1

Answer: (C)

We have,

$PA\cdot PB=9$
Now, $P$ is the mid-point of $AB$ , therefore
$PA=PB\Rightarrow P{A}^2=9\Rightarrow PA=3$
Similarly, $CQ=4$ .
Now, in $\Delta PMA$ ,
$P{M}^2=A{M}^2-A{P}^2$
$\Rightarrow P{M}^2=5^2-3^2$
$\Rightarrow PM=4$
Similarly, in $\Delta CMQ$
$MQ=\sqrt{C{M}^2-C{Q}^2}=\sqrt{5^2-4^2}=3$
Hence,
$PQ=4+3=7$