Question Number 173709 by dragan91 last updated on 16/Jul/22
$$\mathrm{In}\:\mathrm{triangle}\:\bigtriangleup\mathrm{ABC}\:\mathrm{prove}: \\ $$$$\mathrm{cos}\left(\measuredangle\frac{\mathrm{A}}{\mathrm{2}}\right)>\frac{\mathrm{1}}{\mathrm{4}}\centerdot\frac{\mathrm{2a}+\mathrm{b}+\mathrm{c}}{\:\sqrt{\mathrm{R}\left(\mathrm{R}+\mathrm{2r}_{\mathrm{a}} \right)}} \\ $$