List questions from geometric-inequalities

Published on 13 Nov 2020 - 15:24

68

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proving $\min(OR,PR,QR)+OR+PR+QR<OQ+QP+PO$

Published on 21 Nov 2020 - 9:02

201

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If $2$ altitudes of a triangle are $9$ and $40$ then find the minimum perimeter

Published on 24 Nov 2020 - 3:03

63

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If $H$ is the orthocenter and $D,E,F$ are foot of altitudes prove that $\frac{AD}{HD}+\frac{BC}{HE}+\frac{CF}{HF}≥9$

Published on 25 Nov 2020 - 5:58

23

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Side lengths of a triangle satisfy $ab+bc+ca=3$. Prove that $3≤a+b+c≤2√3$

Published on 25 Nov 2020 - 18:04

136

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For $\triangle ABC$ with circumradius $R$ and nine-point center $E$, prove that $EA+EB+EC\le3R$

Published on 16 Dec 2020 - 14:04

146

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What inequalities for convex sets are known since the work of Scott and Awyong?

Published on 03 Jan 2021 - 19:30

260

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

Published on 25 Mar 2026 - 23:21

41

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Inequalities between areas of triangles in an Euclidean 4-simplex?

Published on 05 Feb 2021 - 19:59

88

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Prove that $AG+GB+GH+DH+HE\ge CF.$

Published on 28 Feb 2021 - 9:00

164

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generalized f-mean/power mean inequalities

Published on 08 Mar 2021 - 22:42

220

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Is the "triangle inequality for reciprocals" a sufficient condition for altitudes of a triangle?

Published on 23 Feb 2026 - 22:30

17

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Relation between measures of a subset and its boundary

Published on 30 Mar 2021 - 17:35

245

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Detect if two elliptic cones overlap

Published on 26 Mar 2026 - 3:19

35

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Proving a conditional algebraic inequality

Published on 20 May 2021 - 16:43

List Question

Equivalence of statements via geometric inequality on $4$ Points

proving $\min(OR,PR,QR)+OR+PR+QR<OQ+QP+PO$

If $2$ altitudes of a triangle are $9$ and $40$ then find the minimum perimeter

If $H$ is the orthocenter and $D,E,F$ are foot of altitudes prove that $\frac{AD}{HD}+\frac{BC}{HE}+\frac{CF}{HF}≥9$

Side lengths of a triangle satisfy $ab+bc+ca=3$. Prove that $3≤a+b+c≤2√3$

For $\triangle ABC$ with circumradius $R$ and nine-point center $E$, prove that $EA+EB+EC\le3R$

What inequalities for convex sets are known since the work of Scott and Awyong?

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

Inequalities between areas of triangles in an Euclidean 4-simplex?

Prove that $AG+GB+GH+DH+HE\ge CF.$

generalized f-mean/power mean inequalities

Is the "triangle inequality for reciprocals" a sufficient condition for altitudes of a triangle?

Relation between measures of a subset and its boundary

Detect if two elliptic cones overlap

Proving a conditional algebraic inequality

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