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Take any point O in the interior of a triangle PQR. Is
$(i).\ OP + OQ > PQ?$
$(ii).\ OQ + OR > QR?$
$(iii).\ OR + OP > RP?$"
Given: A triangle PQR.
To do: To take any point O in the interior of a triangle PQR. And to find whether :
$(i).\ OP + OQ > PQ?$
$(ii).\ OQ + OR > QR?$
$(iii).\ OR + OP > RP?$
Solution:
$(i)$. Join $OR$, $OQ$ and $OP$
In $\triangle OPQ$,
$OP+OR>PQ$
yes, the $POQ$ form is a triangle.
$(ii)$ In $\triangle ORQ$
$OQ+OR>QR$
yes, $ORQ$ from a triangle.
$(iii)$ In $\triangle ORP$
$OR+OP>PR$
yes, $ORP$ form a triangle.
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