Question

In $\Delta ABC, $ $O$ is the circumcentre and $H$ is the orthocentre. Then prove that $AH^2 +BC^2 =4AO^2.$

score 256 · Answer 1 · 2016-08-15 13:50:51

256

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In $\Delta ABC, $ $O$ is the circumcentre and $H$ is the orthocentre. Then prove that $AH^2 +BC^2 =4AO^2.$

Published on 15 Aug 2016 - 13:50

score 72 · Answer 2 · 2026-03-26 21:13:59

72

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Why are these two lines not congruent (and other ways to figure out if other shapes are not congruent)

Published on 26 Mar 2026 - 21:13

score 188 · Answer 3 · 2026-03-26 19:18:48

188

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Theorems of properties of rational right triangles proving Pythagorean triples

Published on 26 Mar 2026 - 19:18

score 237 · Answer 4 · 2016-08-17 13:16:58

Equilateral triangles $ABX$ and $CAY$ are described on sides $AB$ and $AC$ of a $\triangle ABC$ externally to $\triangle ABC$. Prove that $CX = BY$.

score 3.4k · Answer 5 · 2016-08-17 14:02:02

3.4k

Views

Find the shortest side if

Published on 17 Aug 2016 - 14:02

score 6.6k · Answer 6 · 2016-08-17 16:23:23

6.6k

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Maximum area of a rectangle inscribed in a triangle is $1/2$ the area of triangle

Published on 17 Aug 2016 - 16:23

score 173 · Answer 7 · 2026-03-29 15:21:30

173

Views

Find the radius of the sector adjoining a triangle

Published on 29 Mar 2026 - 15:21

score 378 · Answer 8 · 2016-08-18 04:11:10

378

Views

Determine the area of triangle PQR in terms of triangle XYZ

Published on 18 Aug 2016 - 4:11

score 60 · Answer 9 · 2016-08-18 04:28:22

60

Views

Solutions of triangles problem

Published on 18 Aug 2016 - 4:28

score 117 · Answer 10 · 2026-03-25 20:36:04

117

Views

How prove this inequality $a^2m_{b}m_{c}+b^2m_{c}m_{a}+c^2m_{a}m_{b}\ge\frac{1}{4}(a^2+b^2+c^2)^2$

Published on 25 Mar 2026 - 20:36

score 63 · Answer 11 · 2026-04-04 09:41:07

63

Views

Find co-ordinate of middle point of BC.

Published on 04 Apr 2026 - 9:41

score 185 · Answer 12 · 2016-08-19 10:10:16

185

Views

I want to prove that for a triangle by side $a, b, c $, Inradius is:$\dfrac{2S}{P}$. Such that $S$ is area and $p$ is semiperimeter.

Published on 19 Aug 2016 - 10:10

score 146 · Answer 13 · 2016-08-19 12:28:09

146

Views

Prove that $ABC$ is right-angled

Published on 19 Aug 2016 - 12:28

score 559 · Answer 14 · 2026-03-25 07:43:36

559

Views

Relationship between Perimeter of 2 Similar Triangle

Published on 25 Mar 2026 - 7:43

score 1.7k · Answer 15 · 2016-08-21 09:44:14

1.7k

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If $S$ is the circumcenter of $\triangle ABC$ and $D, E, F$ are the feet of altitiudes to opposite sides from $A, B, C$, prove that $SB \perp DF$.

Published on 21 Aug 2016 - 9:44

List Question

In $\Delta ABC, $ $O$ is the circumcentre and $H$ is the orthocentre. Then prove that $AH^2 +BC^2 =4AO^2.$

Why are these two lines not congruent (and other ways to figure out if other shapes are not congruent)

Theorems of properties of rational right triangles proving Pythagorean triples

Equilateral triangles $ABX$ and $CAY$ are described on sides $AB$ and $AC$ of a $\triangle ABC$ externally to $\triangle ABC$. Prove that $CX = BY$.

Find the shortest side if

Maximum area of a rectangle inscribed in a triangle is $1/2$ the area of triangle

Find the radius of the sector adjoining a triangle

Determine the area of triangle PQR in terms of triangle XYZ

Solutions of triangles problem

How prove this inequality $a^2m_{b}m_{c}+b^2m_{c}m_{a}+c^2m_{a}m_{b}\ge\frac{1}{4}(a^2+b^2+c^2)^2$

Find co-ordinate of middle point of BC.

I want to prove that for a triangle by side $a, b, c $, Inradius is:$\dfrac{2S}{P}$. Such that $S$ is area and $p$ is semiperimeter.

Prove that $ABC$ is right-angled

Relationship between Perimeter of 2 Similar Triangle

If $S$ is the circumcenter of $\triangle ABC$ and $D, E, F$ are the feet of altitiudes to opposite sides from $A, B, C$, prove that $SB \perp DF$.

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