Given ` A B C` , lines are drawn through `A ,\ B\ a n d\ C` parallel respectively to the sides `B C ,\ C A\ a n d\ A B ,\ ` forming ` P Q Rdot(F igu r e)` .Show that `B C=1/2Q R`

Explanation

"in PQR,

`AB||QC`

`BC||AQ`

so ABCQ is a parallelogram so `BC=AQ`....(1)

similarly in quadrilateral RACB ,`BC=RA`.....(2)

from (1)and (2) `AQ=RA=BC`


so `QR=AQ+RA`

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