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
$PA=PB\Rightarrow PA^{2}=9\Rightarrow PA=3$
Similarly, $CQ=4$ .
Now, in $\Delta PMA$ ,
$PM^{2}=AM^{2}-AP^{2}$
$\Rightarrow PM^{2}=5^{2}-3^{2}$
$\Rightarrow PM=4$
Similarly, in $\Delta CMQ$
$MQ=\sqrt{C M^{2} - C Q^{2}}=\sqrt{5^{2} - 4^{2}}=3$
Hence,
$PQ=4+3=7$