Question

orthocentre and triangle related question

score 512 · Answer 1 · 2026-04-09 12:12:20

512

Views

orthocentre and triangle related question

Published on 09 Apr 2026 - 12:12

score 30 · Answer 2 · 2026-04-15 13:36:57

30

Views

Sorting triangles by hypotenuse length

Published on 15 Apr 2026 - 13:36

score 187 · Answer 3 · 2026-04-13 23:33:51

187

Views

Let $D,E,F$ be (respectively) the projections of $O$ on $BC,CA,AB$. Prove that $\cot{\angle ADB} + \cot{\angle BEC} + \cot{\angle CFA} =0$

Published on 13 Apr 2026 - 23:33

score 1k · Answer 4 · 2026-04-10 17:14:27

1k

Views

The maximum value of $PA\cdot PB\cdot PC$

Published on 10 Apr 2026 - 17:14

score 215 · Answer 5 · 2026-04-15 18:53:57

215

Views

Find max of $S = x\sin^2\angle A + y\sin^2\angle B + z\sin^2\angle C$

Published on 15 Apr 2026 - 18:53

score 50 · Answer 6 · 2026-04-14 12:02:15

Prove that in every acute triangle, the equation stands: $h_c = c \cfrac{\tan(\alpha)\cdot \tan(\beta)}{\tan(\alpha)+\tan(\beta)} $

score 90 · Answer 7 · 2026-04-17 15:16:08

90

Views

Finding all the triangles $ABC$ satisfying $\sum \frac{a^{2}\cos\frac{B-C}{2}}{\sin\frac{A}{2}}=2(a^2+b^2+c^2)$

Published on 17 Apr 2026 - 15:16

score 1.1k · Answer 8 · 2026-04-16 00:27:22

1.1k

Views

Find all triangles with a fixed base and opposite angle

Published on 16 Apr 2026 - 0:27

score 179 · Answer 9 · 2026-04-11 21:30:02

179

Views

Prove that $r^3\rho=2R \rho_1\rho_2 \rho_3$

Published on 11 Apr 2026 - 21:30

score 207 · Answer 10 · 2026-04-16 15:35:06

207

Views

Minimizing the area of the triangles containing a square of side $1$

Published on 16 Apr 2026 - 15:35

score 49 · Answer 11 · 2026-04-16 01:34:22

49

Views

$\frac{CE}{DE}=\frac{(a+b)^2}{kc^2}$

Published on 16 Apr 2026 - 1:34

score 31.1k · Answer 12 · 2026-04-10 21:10:02

31.1k

Views

How do you determine the number of triangles using SSA?

Published on 10 Apr 2026 - 21:10

score 584 · Answer 13 · 2026-04-14 17:44:46

Line joining the orthocenter to the circumcenter of a triangle ABC is inclined to BC at an angle $\tan^{-1}(\frac{3-\tan B\tan C}{\tan B-\tan C})$

score 199 · Answer 14 · 2026-04-16 20:30:01

199

Views

IO is inclined to BC at an angle $\tan^{-1}(\frac{\cos B+\cos C-1}{\sin B-\sin C})$

Published on 16 Apr 2026 - 20:30

score 404 · Answer 15 · 2026-04-16 04:58:33

404

Views

Let $M$ be an arbitrary point located inside the triangle $ABC$. Prove that $\cot\angle MAB + \cot\angle MBC + \cot\angle MCA \geq 3\sqrt{3}$

Published on 16 Apr 2026 - 4:58

List Question

orthocentre and triangle related question

Sorting triangles by hypotenuse length

Let $D,E,F$ be (respectively) the projections of $O$ on $BC,CA,AB$. Prove that $\cot{\angle ADB} + \cot{\angle BEC} + \cot{\angle CFA} =0$

The maximum value of $PA\cdot PB\cdot PC$

Find max of $S = x\sin^2\angle A + y\sin^2\angle B + z\sin^2\angle C$

Prove that in every acute triangle, the equation stands: $h_c = c \cfrac{\tan(\alpha)\cdot \tan(\beta)}{\tan(\alpha)+\tan(\beta)} $

Finding all the triangles $ABC$ satisfying $\sum \frac{a^{2}\cos\frac{B-C}{2}}{\sin\frac{A}{2}}=2(a^2+b^2+c^2)$

Find all triangles with a fixed base and opposite angle

Prove that $r^3\rho=2R \rho_1\rho_2 \rho_3$

Minimizing the area of the triangles containing a square of side $1$

$\frac{CE}{DE}=\frac{(a+b)^2}{kc^2}$

How do you determine the number of triangles using SSA?

Line joining the orthocenter to the circumcenter of a triangle ABC is inclined to BC at an angle $\tan^{-1}(\frac{3-\tan B\tan C}{\tan B-\tan C})$

IO is inclined to BC at an angle $\tan^{-1}(\frac{\cos B+\cos C-1}{\sin B-\sin C})$

Let $M$ be an arbitrary point located inside the triangle $ABC$. Prove that $\cot\angle MAB + \cot\angle MBC + \cot\angle MCA \geq 3\sqrt{3}$

Trending Questions

Popular # Hahtags

Popular Questions