Question

Proof and Geometric intuition of $u \leq 2\ln(1+u)$ for $u \in [0,1]$.

score 112 · Answer 1 · 2026-03-25 19:06:27

112

Views

Proof and Geometric intuition of $u \leq 2\ln(1+u)$ for $u \in [0,1]$.

Published on 25 Mar 2026 - 19:06

score 124 · Answer 2 · 2019-05-06 15:16:22

124

Views

What is wrong with my solution of maximum value of $ \sin \frac {A}{2} + \sin \frac{B}{2} + \sin \frac{C}{2} $ in a triangle ABC?

Published on 06 May 2019 - 15:16

score 150 · Answer 3 · 2026-03-25 06:11:03

150

Views

Prove $a^2b(a-b)+ b^2c(b-c)+ c^2a(c-a)\geq 0$

Published on 25 Mar 2026 - 6:11

score 342 · Answer 4 · 2026-03-25 01:17:23

342

Views

Understanding a Proof: The square root of any metric is ptolemaic..

Published on 25 Mar 2026 - 1:17

score 583 · Answer 5 · 2019-05-29 04:17:49

583

Views

Angle formed by orthocenter, incenter and circumcenter of a triangle $>135^\circ$?

Published on 29 May 2019 - 4:17

score 241 · Answer 6 · 2026-03-25 01:38:30

241

Views

Let $A, B$ and $C$ be the angles of an acute triangle. Show that: $\sin A+\sin B +\sin C > 2$.

Published on 25 Mar 2026 - 1:38

score 30 · Answer 7 · 2019-06-08 20:54:56

30

Views

For acute triangle with sides $a$, $b$, $c$ and circumradius $R$, define $x$, $y$, $z$ with $a+x=b+y=c+z=2R$. Show $x+y+z\lt2R$.

Published on 08 Jun 2019 - 20:54

score 28 · Answer 8 · 2019-06-12 22:14:14

28

Views

$a+OA\lt b+OB\lt c+OC$ when $a\lt b\lt c$ in a triangle

Published on 12 Jun 2019 - 22:14

score 578 · Answer 9 · 2019-06-17 13:50:29

578

Views

If $p$, $q$, $r$ and $s$ are four sides of a quadrilateral, then find the minimum value of $\frac{p^2+ q^2 + r^2}{s^2}$ with logic

Published on 17 Jun 2019 - 13:50

score 167 · Answer 10 · 2019-06-26 02:29:23

167

Views

Find the minimum value of the perimeter

Published on 26 Jun 2019 - 2:29

score 46 · Answer 11 · 2019-06-26 05:11:38

46

Views

$\sqrt{5}BA \leq PA +PB+\sqrt{2}PC$

Published on 26 Jun 2019 - 5:11

score 193 · Answer 12 · 2026-03-25 07:45:51

193

Views

Given three positive numbers $a,b,c$ so that $abc= 1$. Prove $(a-1+\frac{1}{b})(b-1+\frac{1}{c})(c-1+\frac{1}{a})\leqq\frac{2}{a+b+c-1}$ .

Published on 25 Mar 2026 - 7:45

score 57 · Answer 13 · 2019-06-27 16:45:11

57

Views

Can we conclude $0^\circ<A\leq B\leq C<180^\circ$ for any $\triangle ABC$ with $0<a\leq b\leq c$?

Published on 27 Jun 2019 - 16:45

score 327 · Answer 14 · 2026-03-25 07:46:21

327

Views

Given three positive numbers $x,y,z$, prove that $(xyz+x^{2}y+y^{2}z+z^{2}x)^{4}\geqq\frac{256}{27}(x+y+z)^{3}x^{3}y^{3}z^{3}$ .

Published on 25 Mar 2026 - 7:46

score 74 · Answer 15 · 2019-07-14 15:33:49

74

Views

Let $a,b,c$ be the sides of a triangle. The find maximum value $ \frac{A}{S^{2}}$

Published on 14 Jul 2019 - 15:33

List Question

Proof and Geometric intuition of $u \leq 2\ln(1+u)$ for $u \in [0,1]$.

What is wrong with my solution of maximum value of $ \sin \frac {A}{2} + \sin \frac{B}{2} + \sin \frac{C}{2} $ in a triangle ABC?

Prove $a^2b(a-b)+ b^2c(b-c)+ c^2a(c-a)\geq 0$

Understanding a Proof: The square root of any metric is ptolemaic..

Angle formed by orthocenter, incenter and circumcenter of a triangle $>135^\circ$?

Let $A, B$ and $C$ be the angles of an acute triangle. Show that: $\sin A+\sin B +\sin C > 2$.

For acute triangle with sides $a$, $b$, $c$ and circumradius $R$, define $x$, $y$, $z$ with $a+x=b+y=c+z=2R$. Show $x+y+z\lt2R$.

$a+OA\lt b+OB\lt c+OC$ when $a\lt b\lt c$ in a triangle

If $p$, $q$, $r$ and $s$ are four sides of a quadrilateral, then find the minimum value of $\frac{p^2+ q^2 + r^2}{s^2}$ with logic

Find the minimum value of the perimeter

$\sqrt{5}BA \leq PA +PB+\sqrt{2}PC$

Given three positive numbers $a,b,c$ so that $abc= 1$. Prove $(a-1+\frac{1}{b})(b-1+\frac{1}{c})(c-1+\frac{1}{a})\leqq\frac{2}{a+b+c-1}$ .

Can we conclude $0^\circ<A\leq B\leq C<180^\circ$ for any $\triangle ABC$ with $0<a\leq b\leq c$?

Given three positive numbers $x,y,z$, prove that $(xyz+x^{2}y+y^{2}z+z^{2}x)^{4}\geqq\frac{256}{27}(x+y+z)^{3}x^{3}y^{3}z^{3}$ .

Let $a,b,c$ be the sides of a triangle. The find maximum value $ \frac{A}{S^{2}}$

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