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Proofathon Algebra

The time has come! My favorite subject and one of the most highly-requested topics: Proofathon Algebra. We've compiled a nice set of problems for you, so come on and stop by at proofathon.org, and while you're at it, support us on our Facebook page.

For those of you new to Proofathon, we have monthly Olympiad-level proof-based contests that are based on a certain topic each month. There are 8 problems ranging in difficulty from introductory to difficult. Hence, we encourage all to submit solutions to any problems you can do. Good luck, Proofathoners!

Note by Cody Johnson
2 years, 9 months ago

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Here's a problem from the last contest, Geometry:

In \(\triangle ABC\), let \(A_1\) and \(A_2\) be on \(\overline{BC}\) such that \(BA_1=A_1A_2=A_2C\), and define \(B_1\), \(B_2\), \(C_1\), and \(C_2\) similarly. We construct \(A_3\), \(B_3\), and \(C_3\) on the exterior of \(\triangle ABC\) such that \(\triangle A_1A_2A_3\), \(\triangle B_1B_2B_3\), and \(\triangle C_1C_2C_3\) are equilateral triangles. Show that \(\triangle A_3B_3C_3\) is equilateral.

This one comes from Nicolae.

NOTE: This is NOT a live contest problem, so you are free to discuss the problem if you wish. Logan Dymond · 2 years, 9 months ago

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If you share a problem, that would help new members understand what Proofathon problems are like.

P.S. I updated your link to http://proofathon.org. If you do not include http://, then it will link to brilliant.org/proofathon.org. Calvin Lin Staff · 2 years, 9 months ago

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I like how that penultimate line is so original. #IPhOO Ahaan Rungta · 2 years, 9 months ago

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