Question

In given figure, $A,B$ and $C$ are points on $OP,OQ$ and $OR$ respectively such that $AB||PQ$ and $AC||PR$. Show that $BC||QR$.

Answer 1

In $△POR,$

$PR\parallel AC$ Given

$\therefore$ By basic proportionality theorem,

$\frac{PA}{AO}=\frac{RC}{CO}............\left(1\right)$

Similarly,

In $△POQ,$

$AB\parallel PQ$ Given

$\therefore$ By basic proportionality theorem,

$\frac{PA}{AO}=\frac{QB}{BO}............\left(2\right)$

$\therefore$ From $\left(1\right)$ and $\left(2\right)$,

$\frac{RC}{CO}=\frac{QB}{BO}$

$\therefore$ By converse of basic proportionality theorem,

$BC\parallel QR$ $\left[henceproved\right]$