Question Number 198460 by hardmath last updated on 20/Oct/23
$$\mathrm{In}\:\:\:\bigtriangleup\mathrm{ABC}\:\:\:\mathrm{holds}: \\ $$$$\Pi\:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{a}}\:\mathrm{tan}\:\frac{\mathrm{A}}{\mathrm{2}}\right)\:\geqslant\:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{3R}}\right)^{\mathrm{3}} \\ $$