Question

Finding the radius of incircle of $\triangle ABC$ where each of three other circles is mutually tangent to two sides of the triangle respectively

score 38 · Answer 1 · 2019-03-04 03:50:05

38

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Finding the radius of incircle of $\triangle ABC$ where each of three other circles is mutually tangent to two sides of the triangle respectively

Published on 04 Mar 2019 - 3:50

score 4.7k · Answer 2 · 2026-03-28 04:23:22

4.7k

Views

Soft question- The Bashing Technique and Other powerful techniques for Olympiads

Published on 28 Mar 2026 - 4:23

score 744 · Answer 3 · 2026-03-28 13:41:58

744

Views

Example of a non-abelian group $(G,.)$ where $a^2b=ba^2\Rightarrow ab=ba $

Published on 28 Mar 2026 - 13:41

score 76 · Answer 4 · 2019-03-05 10:59:34

76

Views

Inequality with sums and products

Published on 05 Mar 2019 - 10:59

score 95 · Answer 5 · 2019-03-05 20:31:11

95

Views

For $f$ convex $\int_0^af+\int_0^bf+\int_0^cf+\int_0^{a+b+c}f\geq \int_0^{a+b}f+\int_0^{b+c}f+\int_0^{c+a}f$

Published on 05 Mar 2019 - 20:31

score 214 · Answer 6 · 2019-03-06 02:56:46

214

Views

What is the probability that a triangle is obtuse given two points separated by $15^o$ and a third random point that all lie on a circle?

Published on 06 Mar 2019 - 2:56

score 331 · Answer 7 · 2026-03-26 17:52:05

331

Views

Understanding a technique mentioned in 2016 IMO Shortlist

Published on 26 Mar 2026 - 17:52

score 537 · Answer 8 · 2026-03-27 13:25:45

537

Views

Finding the area of inner triangle constructed by three cevian lines of a large triangle

Published on 27 Mar 2026 - 13:25

score 139 · Answer 9 · 2026-03-27 13:27:17

139

Views

Question from an IMC(International mathematics competition) key statge III selection exam

Published on 27 Mar 2026 - 13:27

score 172 · Answer 10 · 2026-03-25 06:26:40

172

Views

Some Cauchy-Schwarz Inequalities

Published on 25 Mar 2026 - 6:26

score 1k · Answer 11 · 2026-03-25 12:13:49

1k

Views

Given three a-triangle-sidelengths $a,b,c$. Prove that $3\left((a^{2}b(a-b)+b^{2}c(b-c)+c^{2}a(c-a)\right)\geqq b(a+b-c)(a-c)(c-b)$ .

Published on 25 Mar 2026 - 12:13

score 278 · Answer 12 · 2026-03-26 14:34:57

278

Views

In a cyclic $\square ABCD$, $BC, CD$ and $DA$ are three tangents of such a circle that its center is on the side $AB$. Proving that $AD + BC = AB$

Published on 26 Mar 2026 - 14:34

score 956 · Answer 13 · 2026-03-25 20:36:18

956

Views

Finding the least possible value of perimeter of $\triangle ABC$ with given ranges of angle

Published on 25 Mar 2026 - 20:36

score 542 · Answer 14 · 2026-03-25 13:56:23

542

Views

If the sides of a quadrilateral are $a,b,c,d$, prove that the area cannot exceed $(ac+bd)/2$.

Published on 25 Mar 2026 - 13:56

score 1.7k · Answer 15 · 2019-03-09 23:11:19

1.7k

Views

Prove that the area of the triangle formed by the medians is equal to $3/4$ the area of the original triangle

Published on 09 Mar 2019 - 23:11

List Question

Finding the radius of incircle of $\triangle ABC$ where each of three other circles is mutually tangent to two sides of the triangle respectively

Soft question- The Bashing Technique and Other powerful techniques for Olympiads

Example of a non-abelian group $(G,.)$ where $a^2b=ba^2\Rightarrow ab=ba $

Inequality with sums and products

For $f$ convex $\int_0^af+\int_0^bf+\int_0^cf+\int_0^{a+b+c}f\geq \int_0^{a+b}f+\int_0^{b+c}f+\int_0^{c+a}f$

What is the probability that a triangle is obtuse given two points separated by $15^o$ and a third random point that all lie on a circle?

Understanding a technique mentioned in 2016 IMO Shortlist

Finding the area of inner triangle constructed by three cevian lines of a large triangle

Question from an IMC(International mathematics competition) key statge III selection exam

Some Cauchy-Schwarz Inequalities

Given three a-triangle-sidelengths $a,b,c$. Prove that $3\left((a^{2}b(a-b)+b^{2}c(b-c)+c^{2}a(c-a)\right)\geqq b(a+b-c)(a-c)(c-b)$ .

In a cyclic $\square ABCD$, $BC, CD$ and $DA$ are three tangents of such a circle that its center is on the side $AB$. Proving that $AD + BC = AB$

Finding the least possible value of perimeter of $\triangle ABC$ with given ranges of angle

If the sides of a quadrilateral are $a,b,c,d$, prove that the area cannot exceed $(ac+bd)/2$.

Prove that the area of the triangle formed by the medians is equal to $3/4$ the area of the original triangle

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