A Multiplicative Identity of Areas in a Triangle

Draw, through point $R$ in the interior of $ABC$, lines $JQ,KM$, and $NP$ parallel to sides $BC,AB$, and $AC$, respectively. 

Let $(\Gamma )$ denotes the area of shape $\Gamma$. Then

$(JMR)(PQR)(KNR)=(JNR)(KQR)(MPR)$.

Proof