Question

Minimal area of a right triangle with inradius $1$

score 506 · Answer 1 · 2026-04-12 17:16:10

506

Views

Minimal area of a right triangle with inradius $1$

Published on 12 Apr 2026 - 17:16

score 125 · Answer 2 · 2026-04-17 07:27:38

125

Views

Let $a,b,c$ be the length of the side $BC,CA,AB$ respectively for $\triangle ABC$. Show that $(2b+2c-2a)^3(a+b+c)\geq18a^2bc$.

Published on 17 Apr 2026 - 7:27

score 72 · Answer 3 · 2026-04-16 19:58:02

72

Views

Draw a graph for the inequality $(x_1 - \frac{1}{2})^2 + (y_1 - \frac{1}{2})^2 < (x_2 - \frac{1}{2})^2 + (y_2 - \frac{1}{2})^2$

Published on 16 Apr 2026 - 19:58

score 71 · Answer 4 · 2026-05-10 15:21:15

71

Views

inequality proving for intersection

Published on 10 May 2026 - 15:21

score 198 · Answer 5 · 2026-04-15 18:13:47

198

Views

Proving $\frac{1}{\sin(A/2)}+\frac{1}{\sin(B/2)}+\frac{1}{\sin(C/2)}\ge 6$, where $A$, $B$, $C$ are angles of a triangle

Published on 15 Apr 2026 - 18:13

score 97 · Answer 6 · 2026-04-12 21:03:45

97

Views

Prove inequality inside a triangle

Published on 12 Apr 2026 - 21:03

score 347 · Answer 7 · 2026-04-17 03:45:04

347

Views

Prove that $\frac{6(a^2 + b^2 + c^2)}{a + b + c} \geq \frac{(a + b)^2}{b + c} + \frac{(b + c)^2}{c + a} + \frac{(a + c)^2}{a + b}$

Published on 17 Apr 2026 - 3:45

score 254 · Answer 8 · 2026-04-13 13:00:39

254

Views

inequality in geometry

Published on 13 Apr 2026 - 13:00

score 118 · Answer 9 · 2026-04-10 09:59:53

118

Views

Inequality about Schur

Published on 10 Apr 2026 - 9:59

score 57 · Answer 10 · 2026-04-16 01:07:02

57

Views

$A_1, A_2\in [AB]$ s.t. $AA_1 < AA_2 < 1$

Published on 16 Apr 2026 - 1:07

score 118 · Answer 11 · 2026-04-15 03:18:24

118

Views

Finding the values of $x$ and $y$ for which $x^2 + y^2$ is a minimum

Published on 15 Apr 2026 - 3:18

score 180 · Answer 12 · 2026-04-15 22:18:19

180

Views

Permutation of points $P_i\in X$ such that $\sum^n_{j=1}|P_{\sigma(j+1)}-P_{\sigma(j)}|^2\leq 8$

Published on 15 Apr 2026 - 22:18

score 130 · Answer 13 · 2026-05-10 14:36:47

130

Views

Show that $\sum_{\text{cyc}} \frac{1}{b^2+c^2+5bc-a^2} \leq \frac{\sqrt3}{8S}$ for a triangle with sides $a$, $b$, $c$ and area $S$

Published on 10 May 2026 - 14:36

score 99 · Answer 14 · 2026-04-15 16:48:05

99

Views

Given triangle sides $a$, $b$, $c$, show $\sum_{\text{cyc}}\frac{a}{a+b}\geq\frac32\prod_{\text{cyc}}(\frac{a}{a+b}+\frac{b}{b+c})$

Published on 15 Apr 2026 - 16:48

score 49 · Answer 15 · 2026-04-15 12:50:34

49

Views

lower and upper bounds on $aA+ bB + cC$ and ${\large{\frac{ab}{l_c}}}+{\large{\frac{bc}{l_a}}}+ {\large{\frac{ca}{l_b}}}$.

Published on 15 Apr 2026 - 12:50

List Question

Minimal area of a right triangle with inradius $1$

Let $a,b,c$ be the length of the side $BC,CA,AB$ respectively for $\triangle ABC$. Show that $(2b+2c-2a)^3(a+b+c)\geq18a^2bc$.

Draw a graph for the inequality $(x_1 - \frac{1}{2})^2 + (y_1 - \frac{1}{2})^2 < (x_2 - \frac{1}{2})^2 + (y_2 - \frac{1}{2})^2$

inequality proving for intersection

Proving $\frac{1}{\sin(A/2)}+\frac{1}{\sin(B/2)}+\frac{1}{\sin(C/2)}\ge 6$, where $A$, $B$, $C$ are angles of a triangle

Prove inequality inside a triangle

Prove that $\frac{6(a^2 + b^2 + c^2)}{a + b + c} \geq \frac{(a + b)^2}{b + c} + \frac{(b + c)^2}{c + a} + \frac{(a + c)^2}{a + b}$

inequality in geometry

Inequality about Schur

$A_1, A_2\in [AB]$ s.t. $AA_1 < AA_2 < 1$

Finding the values of $x$ and $y$ for which $x^2 + y^2$ is a minimum

Permutation of points $P_i\in X$ such that $\sum^n_{j=1}|P_{\sigma(j+1)}-P_{\sigma(j)}|^2\leq 8$

Show that $\sum_{\text{cyc}} \frac{1}{b^2+c^2+5bc-a^2} \leq \frac{\sqrt3}{8S}$ for a triangle with sides $a$, $b$, $c$ and area $S$

Given triangle sides $a$, $b$, $c$, show $\sum_{\text{cyc}}\frac{a}{a+b}\geq\frac32\prod_{\text{cyc}}(\frac{a}{a+b}+\frac{b}{b+c})$

lower and upper bounds on $aA+ bB + cC$ and ${\large{\frac{ab}{l_c}}}+{\large{\frac{bc}{l_a}}}+ {\large{\frac{ca}{l_b}}}$.

Trending Questions

Popular # Hahtags

Popular Questions