For a triangle with sides $$a$$, $$b$$, $$c$$ and angle $$C$$, where the angle $$C$$ subtends the side $$c$$, show that
$$c \geqslant (a+b) \sin \left( \frac C2 \right)$$
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Let us stipulate $$0^\circ < C < 180^\circ$$ and of course $$a,b,c > 0$$. Consequently, $$0^\circ < \frac C2...