How To Apply Rotation/Construction In It

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

Note by Vilakshan Gupta
2 years, 6 months ago

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

The almighty knows it all. - 2 years, 6 months ago

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please explain the solution

Vilakshan Gupta - 2 years, 6 months ago

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Draw AOAO' = OAOA such that OAO=60\angle OAO' = 60^{\circ}. Then ΔOABΔOAC\Delta OAB \cong \Delta O'AC => OBOB == OCO'C . Now, draw (join) OO.OO'. Then clearly ΔOOA\Delta O'OA is equilateral. [=> all \angle = 6060^{\circ}] Therefore, OO=OAOO' = OA Then ΔOOC\Delta OO'C is the required triangle with the side lengths OA,OBOA , OB and OCOC respectively. Now, calculating angles, OOC=AOCAOO\angle O'OC = \angle AOC - \angle AOO' = 12460=64........................124^{\circ} - 60^{\circ} = 64^{\circ}........................

Calculate the rest angles yourself.

The almighty knows it all. - 2 years, 6 months ago

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@The almighty Knows It All. Thank You Rohit. U are really good in geometry.Are You Really 14? And it seems that u are an IMO aspirant

Vilakshan Gupta - 2 years, 6 months 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.

The almighty knows it all. - 2 years, 6 months ago

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@The almighty Knows It All. Of Course, I would surely like to join your team .Please Invite me , my email id is- vilakshangupta2002@gmail.com

Vilakshan Gupta - 2 years, 6 months ago

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

The almighty knows it all. - 2 years, 6 months 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 - 2 years, 3 months ago

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

Satwik Murarka - 2 years, 6 months ago

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ok you can join us by giving your email.

The almighty knows it all. - 2 years, 6 months ago

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@Rohit Camfar satwikmurarka@yahoo.com

Satwik Murarka - 2 years, 6 months ago

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

The almighty knows it all. - 2 years, 5 months ago

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