Question

If $2(bc^2+ca^2+ab^2) = b^2c+c^2a+a^2b+3abc, $ then prove that triangle $ABC$ is equilateral

score 1.7k · Answer 1 · 2026-03-26 03:06:11

1.7k

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If $2(bc^2+ca^2+ab^2) = b^2c+c^2a+a^2b+3abc, $ then prove that triangle $ABC$ is equilateral

Published on 26 Mar 2026 - 3:06

score 416 · Answer 2 · 2016-12-29 23:12:05

416

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Find angles in a right triangle if $\tan\theta = \frac34$, where $\theta$ is the angle between medians

Published on 29 Dec 2016 - 23:12

score 59 · Answer 3 · 2016-12-30 16:35:26

59

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Prove this relation for areas: $2[\triangle BOD] = [\square COME]$

Published on 30 Dec 2016 - 16:35

score 310 · Answer 4 · 2026-03-26 17:52:39

310

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Prove that: $ m_a + m_b + m_c \le 4R + r $

Published on 26 Mar 2026 - 17:52

score 470 · Answer 5 · 2016-12-31 08:04:06

470

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Angles in triangles are in AP, find:$\dfrac{a}{c}\sin 2A+\dfrac{c}{a}\sin 2C$

Published on 31 Dec 2016 - 8:04

score 1.3k · Answer 6 · 2016-12-31 18:01:35

1.3k

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Given length of one side and its median and another median in a triangle. Find area of the triangle

Published on 31 Dec 2016 - 18:01

score 376 · Answer 7 · 2017-01-01 02:20:29

376

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Similar triangles: the shortest side of triangle $B$ measures $6$. Find the other two sides.

Published on 01 Jan 2017 - 2:20

score 87 · Answer 8 · 2017-01-01 18:20:49

87

Views

Proof in Geometry. Is this solution correct?

Published on 01 Jan 2017 - 18:20

score 105 · Answer 9 · 2017-01-02 20:01:00

105

Views

Can I get the triangles area by squares of sides?

Published on 02 Jan 2017 - 20:01

score 22.7k · Answer 10 · 2017-01-03 23:09:12

22.7k

Views

Ratio of Legs in 15, 75, 90 triangles

Published on 03 Jan 2017 - 23:09

score 207 · Answer 11 · 2017-01-04 21:56:50

207

Views

Does the law of cosines imply triangle exists?

Published on 04 Jan 2017 - 21:56

score 540 · Answer 12 · 2026-03-28 04:33:28

540

Views

How to solve the following trig triangle word problem?

Published on 28 Mar 2026 - 4:33

score 3k · Answer 13 · 2017-01-05 07:12:31

3k

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Circumradius of triangle ABC where H is orthocentre and $(AH)(BH)(CH) = 3 $ and $(AH)^2 + (BH)^2 + (CH)^2 = 7 $

Published on 05 Jan 2017 - 7:12

score 1.7k · Answer 14 · 2017-01-05 16:43:53

1.7k

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If, in a triangle, $\cos(A) + \cos(B) + 2\cos(C) = 2$ prove that the sides of the triangle are in AP

Published on 05 Jan 2017 - 16:43

score 899 · Answer 15 · 2017-01-05 16:58:59

899

Views

What does AP mean in the context of triangle proofs?

Published on 05 Jan 2017 - 16:58

List Question

If $2(bc^2+ca^2+ab^2) = b^2c+c^2a+a^2b+3abc, $ then prove that triangle $ABC$ is equilateral

Find angles in a right triangle if $\tan\theta = \frac34$, where $\theta$ is the angle between medians

Prove this relation for areas: $2[\triangle BOD] = [\square COME]$

Prove that: $ m_a + m_b + m_c \le 4R + r $

Angles in triangles are in AP, find:$\dfrac{a}{c}\sin 2A+\dfrac{c}{a}\sin 2C$

Given length of one side and its median and another median in a triangle. Find area of the triangle

Similar triangles: the shortest side of triangle $B$ measures $6$. Find the other two sides.

Proof in Geometry. Is this solution correct?

Can I get the triangles area by squares of sides?

Ratio of Legs in 15, 75, 90 triangles

Does the law of cosines imply triangle exists?

How to solve the following trig triangle word problem?

Circumradius of triangle ABC where H is orthocentre and $(AH)(BH)(CH) = 3 $ and $(AH)^2 + (BH)^2 + (CH)^2 = 7 $

If, in a triangle, $\cos(A) + \cos(B) + 2\cos(C) = 2$ prove that the sides of the triangle are in AP

What does AP mean in the context of triangle proofs?

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