Challenging problem given to 12 year olds – square in a quadrant

Thanks to John H. for the suggestion! A square is inscribed in a quarter circle with two of its vertices on the arc. If the radius equals 1, what is the area of the square? Special thanks this month to: Robert Zarnke, Kyle, Mike Robertson, Michael Anvari, Daniel Lewis. Thanks to all supporters on Patreon! http://www.patreon.com/mindyourdecisions

I thank these people who helped me prove the first step on Twitter:
ahmed_elashraf
https://twitter.com/ahmed_elashraf/status/1450213493798494211
ScottRollison
https://twitter.com/ScottRollison/status/1450251161798430728
OkanAtalay1970

pic.twitter.com/11CCJsLm8i

— Okan Atalay (@OkanAtalay1970) October 19, 2021

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