List questions from geometric-inequalities

Published on 08 Jan 2020 - 15:45

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A point inside a triangle

Published on 10 Jan 2020 - 16:56

81

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For convex cyclic hexagon $ABCDEF$, show $AC\cdot BD \cdot CE \cdot DF \cdot EA\cdot FB \geq 27\cdot AB\cdot BC\cdot CD \cdot DE\cdot EF\cdot FA$

Published on 10 Jan 2020 - 18:25

135

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For △ABC, prove $\frac a{h_a} + \frac b{h_b} + \frac c{h_c} \ge 2 (\tan\frac{\alpha}2+ \tan\frac{\beta}2 + \tan\frac{\gamma}2)$

Published on 27 Jan 2020 - 15:35

51

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Solving Inequality Relation:

Published on 28 Jan 2020 - 17:01

49

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Circular arrangement of numbers with constraint on 3 consecutive triples of them gives a unique solution

Published on 26 Mar 2026 - 6:10

110

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Prove $\prod\limits_{k=1}^N (1+0.8\cdot r_{k})-1\leq \left( \prod\limits_{k=1}^{N}(1+r_{k}) -1 \right)\cdot0.8$

Published on 11 Feb 2020 - 16:48

160

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Prove that $m_a\geq \dfrac{b^2+c^2}{4R}$

Published on 16 Feb 2020 - 19:53

303

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Trouble with sum of inverse integers vs. inverse of sum of integers

Published on 18 Feb 2020 - 1:40

469

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Hard inequality problem (if $(a_2-a_1)^2 + (a_3-a_2)^2 + \ldots + (a_{2n}-a_{2n-1})^2 = 1$ ...)

Published on 22 Feb 2020 - 23:44

250

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In ABC find points X,Y,Z such that AXYZ is rhombus

Published on 28 Feb 2020 - 7:59

92

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Prove that at least one area is less then one quarter of area of ABC

Published on 01 Mar 2020 - 17:25

247

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Distance between mid point of two sides of a quadrilateral

Published on 25 Mar 2026 - 23:10

113

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Triangle's circumcircle inequality: Is it suitable for high schoolers?

Published on 05 Mar 2020 - 0:39

111

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A geometric inequality for acute triangle $\sum \sqrt \frac{b^2+c^2-a^2}{a^2+2bc} \leq \sqrt3$

Published on 14 Mar 2020 - 13:48

List Question

Inequality Solution Correctness

A point inside a triangle

For convex cyclic hexagon $ABCDEF$, show $AC\cdot BD \cdot CE \cdot DF \cdot EA\cdot FB \geq 27\cdot AB\cdot BC\cdot CD \cdot DE\cdot EF\cdot FA$

For △ABC, prove $\frac a{h_a} + \frac b{h_b} + \frac c{h_c} \ge 2 (\tan\frac{\alpha}2+ \tan\frac{\beta}2 + \tan\frac{\gamma}2)$

Solving Inequality Relation:

Circular arrangement of numbers with constraint on 3 consecutive triples of them gives a unique solution

Prove $\prod\limits_{k=1}^N (1+0.8\cdot r_{k})-1\leq \left( \prod\limits_{k=1}^{N}(1+r_{k}) -1 \right)\cdot0.8$

Prove that $m_a\geq \dfrac{b^2+c^2}{4R}$

Trouble with sum of inverse integers vs. inverse of sum of integers

Hard inequality problem (if $(a_2-a_1)^2 + (a_3-a_2)^2 + \ldots + (a_{2n}-a_{2n-1})^2 = 1$ ...)

In ABC find points X,Y,Z such that AXYZ is rhombus

Prove that at least one area is less then one quarter of area of ABC

Distance between mid point of two sides of a quadrilateral

Triangle's circumcircle inequality: Is it suitable for high schoolers?

A geometric inequality for acute triangle $\sum \sqrt \frac{b^2+c^2-a^2}{a^2+2bc} \leq \sqrt3$

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