Question

For all triangle prove that $\sum\limits_{cyc}m_a\cos\frac{\alpha}{2}\geq\frac{3}{4}(a+b+c)$

score 170 · Answer 1 · 2017-01-19 14:58:24

170

Views

For all triangle prove that $\sum\limits_{cyc}m_a\cos\frac{\alpha}{2}\geq\frac{3}{4}(a+b+c)$

Published on 19 Jan 2017 - 14:58

score 98 · Answer 2 · 2017-01-20 17:06:40

98

Views

Prove that $\sum\limits_{cyc}\sin\frac{\alpha}{2}\geq\frac{3}{2}\sqrt[9]{\frac{2r}{R}}$

Published on 20 Jan 2017 - 17:06

score 284 · Answer 3 · 2026-03-25 22:06:17

284

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$\tan {\frac{A}{2}} + \tan {\frac{B}{2}} +\tan{\frac{C}{2}} \geq 4 - \sqrt {3} $

Published on 25 Mar 2026 - 22:06

score 172 · Answer 4 · 2017-01-26 16:28:14

172

Views

Prove that if the sides $a,b,c$ of a triangle satisfy $a^2+b^2=kc^2$, then $k>\frac {1}{2}$.

Published on 26 Jan 2017 - 16:28

score 306 · Answer 5 · 2026-03-25 15:53:39

306

Views

Is this some kind of Holder's inequality?

Published on 25 Mar 2026 - 15:53

score 98 · Answer 6 · 2017-02-03 08:03:53

98

Views

What is the greatest area difference between two "nice triangles"?

Published on 03 Feb 2017 - 8:03

score 156 · Answer 7 · 2017-02-05 05:18:02

156

Views

Inequality on perimeter of inscribed polygon

Published on 05 Feb 2017 - 5:18

score 66 · Answer 8 · 2017-02-05 18:32:40

66

Views

Inequality in a non obtuse triangle

Published on 05 Feb 2017 - 18:32

score 174 · Answer 9 · 2017-02-09 16:57:29

174

Views

Looking for a better (geometric) approximation of $\pi$...

Published on 09 Feb 2017 - 16:57

score 114 · Answer 10 · 2017-02-15 18:15:15

114

Views

If $\displaystyle |z_1| = |z_2| = |z_3| = R$ then prove $ \sum_{z_1, z_2, z_3} |z_1 - z_2|\cdot|z_2 - z_3| \le 9R^2$ for $z_1,z_2,z_3 \in \mathbb{C}$.

Published on 15 Feb 2017 - 18:15

score 104 · Answer 11 · 2017-02-17 14:13:53

104

Views

Inequality concerning segments of an interior point to vertices of a triangle

Published on 17 Feb 2017 - 14:13

score 125 · Answer 12 · 2017-02-20 03:43:36

125

Views

How prove $ax(a+x)+by(b+y)+cz(c+z)\ge 3(abc+xyz)$

Published on 20 Feb 2017 - 3:43

score 192 · Answer 13 · 2017-02-26 16:38:52

192

Views

Question from applications of derivatives.

Published on 26 Feb 2017 - 16:38

score 63 · Answer 14 · 2017-02-28 07:18:24

63

Views

How prove this inequality $\sum\tan{\frac{A}{2}}-\frac{\sqrt{3}-1}{8}\prod\csc{\frac{A}{2}}\le 1$

Published on 28 Feb 2017 - 7:18

score 211 · Answer 15 · 2017-02-28 13:16:31

211

Views

A geometric integral inequality

Published on 28 Feb 2017 - 13:16

List Question

For all triangle prove that $\sum\limits_{cyc}m_a\cos\frac{\alpha}{2}\geq\frac{3}{4}(a+b+c)$

Prove that $\sum\limits_{cyc}\sin\frac{\alpha}{2}\geq\frac{3}{2}\sqrt[9]{\frac{2r}{R}}$

$\tan {\frac{A}{2}} + \tan {\frac{B}{2}} +\tan{\frac{C}{2}} \geq 4 - \sqrt {3} $

Prove that if the sides $a,b,c$ of a triangle satisfy $a^2+b^2=kc^2$, then $k>\frac {1}{2}$.

Is this some kind of Holder's inequality?

What is the greatest area difference between two "nice triangles"?

Inequality on perimeter of inscribed polygon

Inequality in a non obtuse triangle

Looking for a better (geometric) approximation of $\pi$...

If $\displaystyle |z_1| = |z_2| = |z_3| = R$ then prove $ \sum_{z_1, z_2, z_3} |z_1 - z_2|\cdot|z_2 - z_3| \le 9R^2$ for $z_1,z_2,z_3 \in \mathbb{C}$.

Inequality concerning segments of an interior point to vertices of a triangle

How prove $ax(a+x)+by(b+y)+cz(c+z)\ge 3(abc+xyz)$

Question from applications of derivatives.

How prove this inequality $\sum\tan{\frac{A}{2}}-\frac{\sqrt{3}-1}{8}\prod\csc{\frac{A}{2}}\le 1$

A geometric integral inequality

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