Inside an equilateral $\triangle ABC$ lies a point $O$. It is known that $\angle AOB=113^{\circ}$ and $\angle BOC=123^{\circ}$. Find the angles of the triangle whose sides are equal to segments $OA,OB,OC$.

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

@Vilakshan Gupta
–
Yep, 'm an IMO aspirant, hoping for it but it is never going to be easy at all. If you too are an IMO aspirant then would you like to join our RMO / INMO prperation team at Slack.

@Vilakshan Gupta
–
Hi guys @Vilakshan Gupta@Satwik Murarka I would also like to join you guy's team. Here is the email imjabitg@gmail.com I had asked @Rohit Camfaron a different forum but he told that he is no more in the team and asked me to ask on this notice board.

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:

TopNewest@Rohit Camfar satwikmurarka@yahoo.com

Log in to reply

Ok you are invited you can join us now by going into your Id

Log in to reply

@Rohit Camfar Can I join the RMO preparation team?I am also an RMO aspirant.

Log in to reply

ok you can join us by giving your email.

Log in to reply

The angle in their correct order are 64 , 53 , 63.

Log in to reply

please explain the solution

Log in to reply

Draw $AO'$ = $OA$ such that $\angle OAO' = 60^{\circ}$. Then $\Delta OAB \cong \Delta O'AC$ => $OB$ $=$ $O'C$ . Now, draw (join) $OO'.$ Then clearly $\Delta O'OA$ is equilateral. [=> all $\angle$ = $60^{\circ}$] Therefore, $OO' = OA$ Then $\Delta OO'C$ is the required triangle with the side lengths $OA , OB$ and $OC$ respectively. Now, calculating angles, $\angle O'OC = \angle AOC - \angle AOO'$ = $124^{\circ} - 60^{\circ} = 64^{\circ}........................$

Calculate the rest angles yourself.

Log in to reply

Log in to reply

Log in to reply

Log in to reply

@Vilakshan Gupta @Satwik Murarka I would also like to join you guy's team. Here is the email imjabitg@gmail.com I had asked @Rohit Camfaron a different forum but he told that he is no more in the team and asked me to ask on this notice board.

Hi guysLog in to reply

Log in to reply