Question

Systems of linear homogenous inequalities: getting started

score 34 · Answer 1 · 2026-03-27 17:06:33

34

Views

Systems of linear homogenous inequalities: getting started

Published on 27 Mar 2026 - 17:06

score 306 · Answer 2 · 2026-02-24 01:54:40

306

Views

Prove that if $a,b,c$ are sides of a triangle and $s$ is the semi-perimeter, then $a^2+b^2+c^2 \geq \dfrac{36}{35}\bigg(s^2 + \dfrac{abc}{s}\bigg)$

Published on 24 Feb 2026 - 1:54

score 123 · Answer 3 · 2021-07-25 11:01:47

123

Views

Given $a,b,c$ are sides of a triangle, Prove that :- $\frac{1}{3} \leq \frac{a^2+b^2+c^2}{(a+b+c)^2} < \frac{1}{2}$

Published on 25 Jul 2021 - 11:01

score 143 · Answer 4 · 2021-07-29 21:02:42

143

Views

Does this class of triangles satisfy a certain geometric inequality?

Published on 29 Jul 2021 - 21:02

score 243 · Answer 5 · 2026-03-26 01:04:48

243

Views

Show that $ \frac{x^2}{\sqrt{x^2+y^2}} + \frac{y^2}{\sqrt{y^2+z^2}} + \frac{z^2}{\sqrt{z^2+x^2}} \geq \frac{1}{\sqrt{2}}(x+y+z) $

Published on 26 Mar 2026 - 1:04

score 40 · Answer 6 · 2026-03-26 01:04:50

40

Views

Let $h_{1},h_{2},h_{3}$ be the altitudes and $m_{1},m_{2},m_{3}$ be the medians of the triangle ABC.

Published on 26 Mar 2026 - 1:04

score 134 · Answer 7 · 2021-08-14 13:39:16

134

Views

Show that $\frac{P_a}{a^2}+\frac{P_b}{b^2}+\frac{P_c}{c^2}\ge\frac{3}{4R}$. When is the equality reached?

Published on 14 Aug 2021 - 13:39

score 93 · Answer 8 · 2021-08-17 06:23:27

93

Views

Bounds of an Expression

Published on 17 Aug 2021 - 6:23

score 224 · Answer 9 · 2021-08-31 04:50:51

224

Views

For an acute angled triangle $ABC,$ if $p=\frac{\sqrt3+\sin A+\sin B+\sin C}{2\sin A\sin B\sin C}$, find the range of $p$

Published on 31 Aug 2021 - 4:50

score 1.1k · Answer 10 · 2021-09-06 14:48:26

1.1k

Views

Largest possible side of a triangle when $\cos(3P)+ \cos(3Q)+ \cos(3R) = 1$.

Published on 06 Sep 2021 - 14:48

score 245 · Answer 11 · 2026-03-25 19:11:45

245

Views

Given the triangle ABC. Let BC = a, AC = b, AB = c. Find the minimum value of the following expression

Published on 25 Mar 2026 - 19:11

score 157 · Answer 12 · 2026-03-25 18:49:37

157

Views

In triangle. Prove that: $2(a+b+c)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\ge9+\sum_{cyc}{\sqrt{17+\frac{4(b+c)((b-c)^2-a^2)}{abc}}}$

Published on 25 Mar 2026 - 18:49

score 140 · Answer 13 · 2021-10-14 11:52:13

140

Views

Prove that $\frac{a+b}{c}+\frac{b+c}{a}+\frac{c+a}{b}\ge a+b+c+\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}$ if $a^2+b^2+c^2+abc=4$.

Published on 14 Oct 2021 - 11:52

score 104 · Answer 14 · 2021-11-14 02:46:50

104

Views

Determining all $(a,b)$ on the unit circle such that $2x+3y+1\le a(x+2)+b(y+3)$ for all $(x,y)$ in the unit disk

Published on 14 Nov 2021 - 2:46

score 303 · Answer 15 · 2021-12-01 12:01:21

303

Views

How to show an inequality in an inner product space?

Published on 01 Dec 2021 - 12:01

List Question

Systems of linear homogenous inequalities: getting started

Prove that if $a,b,c$ are sides of a triangle and $s$ is the semi-perimeter, then $a^2+b^2+c^2 \geq \dfrac{36}{35}\bigg(s^2 + \dfrac{abc}{s}\bigg)$

Given $a,b,c$ are sides of a triangle, Prove that :- $\frac{1}{3} \leq \frac{a^2+b^2+c^2}{(a+b+c)^2} < \frac{1}{2}$

Does this class of triangles satisfy a certain geometric inequality?

Show that $ \frac{x^2}{\sqrt{x^2+y^2}} + \frac{y^2}{\sqrt{y^2+z^2}} + \frac{z^2}{\sqrt{z^2+x^2}} \geq \frac{1}{\sqrt{2}}(x+y+z) $

Let $h_{1},h_{2},h_{3}$ be the altitudes and $m_{1},m_{2},m_{3}$ be the medians of the triangle ABC.

Show that $\frac{P_a}{a^2}+\frac{P_b}{b^2}+\frac{P_c}{c^2}\ge\frac{3}{4R}$. When is the equality reached?

Bounds of an Expression

For an acute angled triangle $ABC,$ if $p=\frac{\sqrt3+\sin A+\sin B+\sin C}{2\sin A\sin B\sin C}$, find the range of $p$

Largest possible side of a triangle when $\cos(3P)+ \cos(3Q)+ \cos(3R) = 1$.

Given the triangle ABC. Let BC = a, AC = b, AB = c. Find the minimum value of the following expression

In triangle. Prove that: $2(a+b+c)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\ge9+\sum_{cyc}{\sqrt{17+\frac{4(b+c)((b-c)^2-a^2)}{abc}}}$

Prove that $\frac{a+b}{c}+\frac{b+c}{a}+\frac{c+a}{b}\ge a+b+c+\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}$ if $a^2+b^2+c^2+abc=4$.

Determining all $(a,b)$ on the unit circle such that $2x+3y+1\le a(x+2)+b(y+3)$ for all $(x,y)$ in the unit disk

How to show an inequality in an inner product space?

Trending Questions

Popular # Hahtags

Popular Questions