Question

$O$ is the centre of the circle with radius $5cm.$ Chords $AB$ and $CD$ are parallel. $AB=6cm$ and $CD=8cm.$ If $PQ$ is distance between $AB$ and $CD,$ then find $PQ.$

Answer 1

$ApplyingPythagorastheoremin\angle AOPand\Delta COQ$

$In\angle AOP,A{O}^2=A{P}^2+P{O}^2\Rightarrow A{O}^2={\left(A{B}^2\right)}^2+P{O}^2{\left(5\right)}^2={\left(4\right)}^2+x^2\Rightarrow 25-16=x^2\therefore x=\sqrt{9}=3cm$

$In\Delta COQ,C{O}^2=O{Q}^2+C{Q}^2\Rightarrow C{O}^2=O{Q}^2+{\left(C{D}^2\right)}^2\Rightarrow 25-9=y^2\Rightarrow y=\sqrt{16}=4cm$

$Therefore,PQ=PO+OQ=3+4=7cm$