Challenging problem given to students - 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!   / mindyourdecisions  

I thank these people who helped me prove the first step on Twitter:
ahmed_elashraf
  / 1450213493798494211  
ScottRollison
  / 1450251161798430728  
OkanAtalay1970
  / 1450305206378434562  

Subscribe: https://www.youtube.com/user/MindYour...

Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas!

If you buy from the links below I may receive a commission for sales. (As an Amazon Associate I earn from qualifying purchases.) This has no effect on the price for you.

Book ratings are from June 2021.

My Books (worldwide links)
https://mindyourdecisions.com/blog/my...

My Books (US links)
Mind Your Decisions: Five Book Compilation
https://amzn.to/2pbJ4wR
A collection of 5 books:
"The Joy of Game Theory" rated 4.2/5 stars on 200 reviews
http://amzn.to/1uQvA20
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4/5 stars on 17 reviews
http://amzn.to/1o3FaAg
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.1/5 stars on 30 reviews
http://amzn.to/1LOCI4U
"The Best Mental Math Tricks" rated 4.2/5 stars on 57 reviews
http://amzn.to/18maAdo
"Multiply Numbers By Drawing Lines" rated 4.1/5 stars on 23 reviews
http://amzn.to/XRm7M4

Mind Your Puzzles: Collection Of Volumes 1 To 3
https://amzn.to/2mMdrJr
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 75 reviews
http://amzn.to/1GhUUSH
"Math Puzzles Volume 2" rated 4.3/5 stars on 21 reviews
http://amzn.to/1NKbyCs
"Math Puzzles Volume 3" rated 4.3/5 stars on 17 reviews
http://amzn.to/1NKbGlp

2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.

My Blog
https://mindyourdecisions.com/blog/

Twitter
  / preshtalwalkar  

Merch
https://teespring.com/stores/mind-you...

Patreon
  / mindyourdecisions  

Press
https://mindyourdecisions.com/blog/press