Page 28 - MATINF Nr. 9-10

28 M. Bencze

Corollary 11. In any triangle ABC hold the following inequalities:

A √
sin
P 2 3 2R
1) ≤ √ ;
B C 2 2R + r
cos 2 + cos 2
2 2
A
sin 3
P 2 2R − r
2) ≤ p ;
B C 2 2R(2R + r)
cos 2 + cos 2
2 2
A √
cos
P 2 s 2R
3) ≤ √ ;
B C 2r 2R + r
cos 2 + cos
2 2
A √
sin 2
P 2 (4R + r) 2R
4) Å ã ≤ √ .
B C A 2s 2R + r
cos 2 + cos 2 cos
2 2 2

References

[1] Octogon Mathematical Magazine (1993-2021).