Question

How prove $\dfrac{|AB|}{|AC|}\le\sqrt{2}+1$

score 118 · Answer 1 · 2017-03-06 07:35:19

118

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How prove $\dfrac{|AB|}{|AC|}\le\sqrt{2}+1$

Published on 06 Mar 2017 - 7:35

score 177 · Answer 2 · 2017-03-08 06:52:27

177

Views

Proof of inequality of area for quadrilateral

Published on 08 Mar 2017 - 6:52

score 77 · Answer 3 · 2017-03-15 15:13:57

77

Views

Bounding the Sum of Distances between Binary Vectors

Published on 15 Mar 2017 - 15:13

score 69 · Answer 4 · 2017-03-17 19:03:31

69

Views

Prove that $MA\cdot AN+NB\cdot BL+LC\cdot CM<BC^2$.

Published on 17 Mar 2017 - 19:03

score 5.2k · Answer 5 · 2017-03-28 11:51:03

5.2k

Views

Prove that the sum of the medians of a triangle is greater than the semiperimeter

Published on 28 Mar 2017 - 11:51

score 37 · Answer 6 · 2017-04-08 07:45:14

37

Views

Solving $n\sum_{i=0}^n \frac{1}{m_i^2} > (\sum_{i=0}^n \frac{1}{m_i})^2 > (n-1)\sum_{i=0}^n \frac{1}{m_i^2}$

Published on 08 Apr 2017 - 7:45

score 476 · Answer 7 · 2017-04-08 09:20:33

476

Views

Proving an inequality involving taxicab distances

Published on 08 Apr 2017 - 9:20

score 100 · Answer 8 · 2023-02-14 11:56:34

100

Views

Magnitude of sum of vectors $\le2$

Published on 14 Feb 2023 - 11:56

score 115 · Answer 9 · 2023-04-19 13:32:21

115

Views

Sum of sides of a quadrilateral and sum of its diagonals

Published on 19 Apr 2023 - 13:32

score 71 · Answer 10 · 2023-04-24 16:30:54

71

Views

Geometric inequalities using sides, radius and semi-perimeter

Published on 24 Apr 2023 - 16:30

score 97 · Answer 11 · 2023-05-02 17:56:15

97

Views

In the plane there are given vectors $a, b, c, d, $, the sum of which is equal to $0$. Prove the inequality!

Published on 02 May 2023 - 17:56

score 50 · Answer 12 · 2023-08-27 22:12:40

50

Views

Longest diagonal in a convex quadrilateral

Published on 27 Aug 2023 - 22:12

score 406 · Answer 13 · 2023-10-01 16:26:23

406

Views

Inequality in an acute-angled triangle

Published on 01 Oct 2023 - 16:26

score 93 · Answer 14 · 2024-03-14 12:59:06

93

Views

In a triangle if $P\left(\frac{1}{a-b+x}+\frac{1}{b-c+x} \ge \frac{1}{c-a+x}\right)=\frac{1}{2}$ then $x=\pm\frac{3}{4}, \pm\frac{3}{5}$ or $0$?

Published on 14 Mar 2024 - 12:59

score 2.7k · Answer 15 · 2015-02-19 12:28:14

2.7k

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Let $a$, $b$ and $c$ be the three sides of a triangle. Show that $\frac{a}{b+c-a}+\frac{b}{c+a-b} + \frac{c}{a+b-c}\geqslant3$.

Published on 19 Feb 2015 - 12:28

List Question

How prove $\dfrac{|AB|}{|AC|}\le\sqrt{2}+1$

Proof of inequality of area for quadrilateral

Bounding the Sum of Distances between Binary Vectors

Prove that $MA\cdot AN+NB\cdot BL+LC\cdot CM<BC^2$.

Prove that the sum of the medians of a triangle is greater than the semiperimeter

Solving $n\sum_{i=0}^n \frac{1}{m_i^2} > (\sum_{i=0}^n \frac{1}{m_i})^2 > (n-1)\sum_{i=0}^n \frac{1}{m_i^2}$

Proving an inequality involving taxicab distances

Magnitude of sum of vectors $\le2$

Sum of sides of a quadrilateral and sum of its diagonals

Geometric inequalities using sides, radius and semi-perimeter

In the plane there are given vectors $a, b, c, d, $, the sum of which is equal to $0$. Prove the inequality!

Longest diagonal in a convex quadrilateral

Inequality in an acute-angled triangle

In a triangle if $P\left(\frac{1}{a-b+x}+\frac{1}{b-c+x} \ge \frac{1}{c-a+x}\right)=\frac{1}{2}$ then $x=\pm\frac{3}{4}, \pm\frac{3}{5}$ or $0$?

Let $a$, $b$ and $c$ be the three sides of a triangle. Show that $\frac{a}{b+c-a}+\frac{b}{c+a-b} + \frac{c}{a+b-c}\geqslant3$.

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