Question

What is the length of a side of square $DCEF$ where $AB=3, BC=4, AC=5$ in the following diagram?

score 63 · Answer 1 · 2019-09-18 18:00:21

63

Views

What is the length of a side of square $DCEF$ where $AB=3, BC=4, AC=5$ in the following diagram?

Published on 18 Sep 2019 - 18:00

score 165 · Answer 2 · 2019-09-20 09:57:31

165

Views

A triangle with all its vertices on one line would still be a triangle, but a degenerate one. Does it matter though?

Published on 20 Sep 2019 - 9:57

score 972 · Answer 3 · 2019-09-22 18:19:12

972

Views

Triangle with angles 30⁰,45⁰,105⁰, find area

Published on 22 Sep 2019 - 18:19

score 133 · Answer 4 · 2019-09-22 23:35:15

133

Views

Given concurrent cevians $AD$, $BE$, $CF$ of $\triangle ABC$, show $\text{area }\triangle DEF\leq \tfrac14\text{}\triangle ABC$

Published on 22 Sep 2019 - 23:35

score 109 · Answer 5 · 2026-03-27 02:50:51

109

Views

reverse proof of sin30 = 1/2 without trigonometry

Published on 27 Mar 2026 - 2:50

score 107 · Answer 6 · 2019-09-24 07:27:06

107

Views

There is a triangle, sides = a,b,c and its angle = $\alpha, \beta, \gamma$

Published on 24 Sep 2019 - 7:27

score 2.1k · Answer 7 · 2026-03-25 23:16:27

2.1k

Views

Find area of shaded regions in a triangle

Published on 25 Mar 2026 - 23:16

score 21 · Answer 8 · 2019-09-25 18:36:25

The side of an equilateral triangle ABC is 4 times square root of 3. The triangle bisectors AM and CN meet at point O. Find vectors AM and CO

score 298 · Answer 9 · 2019-09-25 19:02:23

298

Views

In acute angle triangle, prove that $\cos (A-B) \cos (B-C) \cos (C-A)\ge 8\cos A \cos B \cos C$

Published on 25 Sep 2019 - 19:02

score 82 · Answer 10 · 2019-09-25 20:04:57

82

Views

In $\triangle ABC$, $AD$ and $BE$ are medians, and $AD \perp BE$. If $AC=14$ and $BC=22$, find $AB$.

Published on 25 Sep 2019 - 20:04

score 586 · Answer 11 · 2019-09-26 06:02:08

586

Views

Prove that $\tan\frac{\pi}{9}+ 4\sin\frac{\pi}{9}= \sqrt{3}$ .

Published on 26 Sep 2019 - 6:02

score 66 · Answer 12 · 2019-09-26 23:50:39

66

Views

Triangle Problem with Triangle Congruency

Published on 26 Sep 2019 - 23:50

score 61 · Answer 13 · 2019-09-27 00:13:33

61

Views

If $a$, $b$, $c$ are sides of a triangle, and the system $x^2-ax+b^2+ac-y=0$, $ax+bc-y=0$ has one solution, classify the triangle

Published on 27 Sep 2019 - 0:13

score 226 · Answer 14 · 2019-09-27 16:37:45

226

Views

Prove that the tangent of $(ABC)$ at point $F$ passes through the midpoint of $KJ$.

Published on 27 Sep 2019 - 16:37

score 111 · Answer 15 · 2026-03-25 23:37:52

111

Views

$\sum_{cyclic}\frac{\sqrt{b+c-a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}\leq 3$

Published on 25 Mar 2026 - 23:37

List Question

What is the length of a side of square $DCEF$ where $AB=3, BC=4, AC=5$ in the following diagram?

A triangle with all its vertices on one line would still be a triangle, but a degenerate one. Does it matter though?

Triangle with angles 30⁰,45⁰,105⁰, find area

Given concurrent cevians $AD$, $BE$, $CF$ of $\triangle ABC$, show $\text{area }\triangle DEF\leq \tfrac14\text{}\triangle ABC$

reverse proof of sin30 = 1/2 without trigonometry

There is a triangle, sides = a,b,c and its angle = $\alpha, \beta, \gamma$

Find area of shaded regions in a triangle

The side of an equilateral triangle ABC is 4 times square root of 3. The triangle bisectors AM and CN meet at point O. Find vectors AM and CO

In acute angle triangle, prove that $\cos (A-B) \cos (B-C) \cos (C-A)\ge 8\cos A \cos B \cos C$

In $\triangle ABC$, $AD$ and $BE$ are medians, and $AD \perp BE$. If $AC=14$ and $BC=22$, find $AB$.

Prove that $\tan\frac{\pi}{9}+ 4\sin\frac{\pi}{9}= \sqrt{3}$ .

Triangle Problem with Triangle Congruency

If $a$, $b$, $c$ are sides of a triangle, and the system $x^2-ax+b^2+ac-y=0$, $ax+bc-y=0$ has one solution, classify the triangle

Prove that the tangent of $(ABC)$ at point $F$ passes through the midpoint of $KJ$.

$\sum_{cyclic}\frac{\sqrt{b+c-a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}\leq 3$

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