Question

Sine rule exam question (with $\sin 2 \theta$ term)

score 69 · Answer 1 · 2019-11-22 17:16:03

69

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Sine rule exam question (with $\sin 2 \theta$ term)

Published on 22 Nov 2019 - 17:16

score 34 · Answer 2 · 2019-11-23 07:02:54

34

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Find side length $a$ of triangle given $\cos(2α − β) + \sin(α + β) = 2$ and $b = 2\sqrt3$

Published on 23 Nov 2019 - 7:02

score 147 · Answer 3 · 2019-11-23 18:11:09

147

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Proving two lines are parallel

Published on 23 Nov 2019 - 18:11

score 367 · Answer 4 · 2019-11-24 07:47:10

367

Views

In $\triangle ABC$, if length of medians $BE$ and $CF$ are $12$ and $9$ respectively. Find $\triangle_{max}$

Published on 24 Nov 2019 - 7:47

score 475 · Answer 5 · 2019-11-24 09:05:59

475

Views

Semi-circle inside of a square

Published on 24 Nov 2019 - 9:05

score 13 · Answer 6 · 2019-11-24 22:00:03

Geometry: given a fixed area and vertex angle, prove that an isosceles triangle would minimize the length of the base

score 46 · Answer 7 · 2019-11-25 03:43:52

46

Views

Triangle $ABC$ where $a+c=12$, $b+c=13$, $\angle A = 60^{\circ}$, what is $a^{2} + b^{2} + c^{2}$?

Published on 25 Nov 2019 - 3:43

score 76 · Answer 8 · 2019-11-25 06:43:26

76

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In a triangle, the lengths of the two sides are 6 and 3 cm. Find the length of the third side if the half-sum...

Published on 25 Nov 2019 - 6:43

score 330 · Answer 9 · 2019-11-25 14:21:21

330

Views

In a triangle, if $\tan(A/2)$, $\tan(B/2)$, $\tan(C/2)$ are in arithmetic progression, then so are $\cos A$, $\cos B$, $\cos C$

Published on 25 Nov 2019 - 14:21

score 97 · Answer 10 · 2019-11-25 18:36:16

Triangle sides $a,b,c$ are in arithmetic progression. Show $\sin^2(A/2)\csc2A$, $\sin^2(B/2)\csc2B$, $\sin^2(C/2)\csc2C$ are in harmonic progression

score 452 · Answer 11 · 2019-11-26 09:58:08

If I be the incenter of the triangle ABC and $x,y,z$ the circum radii of the triangles IBC,ICA & IAB, show that $4R^3-R(x^2+y^2+z^2)-xyz = 0$

score 45 · Answer 12 · 2019-11-26 13:52:10

45

Views

Find $p+q$, if area of the triangle ABC can be expressed in terms of $\dfrac{p}{q}$ for the following conditions.

Published on 26 Nov 2019 - 13:52

score 97 · Answer 13 · 2026-03-26 08:14:28

97

Views

Prove that in any triangle

Published on 26 Mar 2026 - 8:14

score 95 · Answer 14 · 2026-03-26 06:34:44

95

Views

If $\triangle$ is the area of triangle with side lengths $a,b,c$, then show that $\triangle \le\dfrac{1}{4}\cdot\sqrt{(a+b+c)abc}$

Published on 26 Mar 2026 - 6:34

score 113 · Answer 15 · 2019-11-27 16:12:09

113

Views

How to find the base of an isosceles triangle with the two equal sides and their medians known

Published on 27 Nov 2019 - 16:12

List Question

Sine rule exam question (with $\sin 2 \theta$ term)

Find side length $a$ of triangle given $\cos(2α − β) + \sin(α + β) = 2$ and $b = 2\sqrt3$

Proving two lines are parallel

In $\triangle ABC$, if length of medians $BE$ and $CF$ are $12$ and $9$ respectively. Find $\triangle_{max}$

Semi-circle inside of a square

Geometry: given a fixed area and vertex angle, prove that an isosceles triangle would minimize the length of the base

Triangle $ABC$ where $a+c=12$, $b+c=13$, $\angle A = 60^{\circ}$, what is $a^{2} + b^{2} + c^{2}$?

In a triangle, the lengths of the two sides are 6 and 3 cm. Find the length of the third side if the half-sum...

In a triangle, if $\tan(A/2)$, $\tan(B/2)$, $\tan(C/2)$ are in arithmetic progression, then so are $\cos A$, $\cos B$, $\cos C$

Triangle sides $a,b,c$ are in arithmetic progression. Show $\sin^2(A/2)\csc2A$, $\sin^2(B/2)\csc2B$, $\sin^2(C/2)\csc2C$ are in harmonic progression

If I be the incenter of the triangle ABC and $x,y,z$ the circum radii of the triangles IBC,ICA & IAB, show that $4R^3-R(x^2+y^2+z^2)-xyz = 0$

Find $p+q$, if area of the triangle ABC can be expressed in terms of $\dfrac{p}{q}$ for the following conditions.

Prove that in any triangle

If $\triangle$ is the area of triangle with side lengths $a,b,c$, then show that $\triangle \le\dfrac{1}{4}\cdot\sqrt{(a+b+c)abc}$

How to find the base of an isosceles triangle with the two equal sides and their medians known

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