This discussion board is a place to discuss our Daily Challenges and the math and science
related to those challenges. Explanations are more than just a solution — they should
explain the steps and thinking strategies that you used to obtain the solution. Comments
should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .

Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.

Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown

Appears as

*italics* or _italics_

italics

**bold** or __bold__

bold

- bulleted - list

bulleted

list

1. numbered 2. list

numbered

list

Note: you must add a full line of space before and after lists for them to show up correctly

Take a point $O$ from which three line segments $OA, OB, OC$, lying on the same plane, emanate such that their respective lengths are $a, b, c$ and the angle between any two of them is 120 degrees. Use Cosine rule and the mentioned equations to find $AB, BC, CA$ which will have values 3,4 and 5 units. Now this triangle $ABC$ is right angled( by the converse of Pythagoras' Theorem), so it's area will be 6 sq. units. Also, the area of the three triangles $AOB, BOC, COA$ can be found out by the sine rule (individually), and now equate it with the earlier found area. The answer comes out to be $8 \sqrt{3}$. [ the calculations are to be done by you].

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in`\(`

...`\)`

or`\[`

...`\]`

to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestTake a point $O$ from which three line segments $OA, OB, OC$, lying on the same plane, emanate such that their respective lengths are $a, b, c$ and the angle between any two of them is 120 degrees. Use Cosine rule and the mentioned equations to find $AB, BC, CA$ which will have values 3,4 and 5 units. Now this triangle $ABC$ is right angled( by the converse of Pythagoras' Theorem), so it's area will be 6 sq. units. Also, the area of the three triangles $AOB, BOC, COA$ can be found out by the sine rule (individually), and now equate it with the earlier found area. The answer comes out to be $8 \sqrt{3}$. [ the calculations are to be done by you].

Log in to reply

Well, your idea is interesting, but are you sure about the value of ab + bc +ac? shouldn' it be 8*sqrt(3)? Could you chek it again, plz??

Log in to reply

Edited.

Log in to reply

Log in to reply

Log in to reply

Could you show any algebraic, only algebraic solution, friend?

Log in to reply

Is it possible to solve this algebraically?

Log in to reply

what will be the algebric solution Help me

Log in to reply

The solution could be algebraical or geometrical, Thanks in advance for help!

Log in to reply

The point "O" is known as "Fermat" or Torricelli Point of the triangle.

Log in to reply