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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 \(OA,OB,OC\).

Note by Vilakshan Gupta
7 months, 2 weeks ago

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@Rohit Camfar satwikmurarka@yahoo.com

Satwik Murarka - 7 months, 1 week ago

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

Rohit Camfar - 7 months ago

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

Satwik Murarka - 7 months, 1 week ago

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ok you can join us by giving your email.

Rohit Camfar - 7 months, 1 week ago

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

Rohit Camfar - 7 months, 2 weeks ago

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please explain the solution

Vilakshan Gupta - 7 months, 2 weeks ago

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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.

Rohit Camfar - 7 months, 2 weeks ago

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@Rohit Camfar Thank You Rohit. U are really good in geometry.Are You Really 14? And it seems that u are an IMO aspirant

Vilakshan Gupta - 7 months, 2 weeks ago

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@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.

Rohit Camfar - 7 months, 2 weeks ago

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@Rohit Camfar Of Course, I would surely like to join your team .Please Invite me , my email id is- vilakshangupta2002@gmail.com

Vilakshan Gupta - 7 months, 2 weeks ago

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@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.

Abhiyudya Kumari - 5 months ago

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@Vilakshan Gupta You have been invited on the team. Check your email and join us.

Rohit Camfar - 7 months, 2 weeks ago

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