Question

Take any point O in the interior of a triangle PQR:
Is OP + OQ > PQ?
Is OP + OR > PR?
Is OQ+ OR > QR?

Answer 1

Join OR, OQ and OP.
POQ forms a triangle.
Since in a triangle sum of the lengths of any two sides would be greater than the length of the third side
=> OP + OQ > PQ
Similarly,
OP + OR > PR; using triangle inquality in $\Delta$ OPR
and
OQ+ OR > QR; using triangle inquality in $\Delta$ OQR

So, all three inequalities given in the question hold true.