Incredibly hard geometry problem from Russia скачать в хорошем качестве

Incredibly hard geometry problem from Russia

This challenging problem was given to students in Russia, but it stumped me! The question was presented as text only--no diagram. Also, the problem was part of an entrance exam for a selective high school. Can you solve it? From each corner of a parallelogram, draw two line segments to connect the corner to the midpoints of the opposite sides. These eight line segments bound an octagon. What is the ratio of the octagon’s area to the parallelogram’s area? Thanks to Michael K. for suggesting the problem and sending the solution! My blog post for this video (also links to many other solutions): https://wp.me/p6aMk-5k7 Here's another solution write-up using symmetry by Bob Corns: https://docs.google.com/document/d/1t... Here's a solution from Reuven BarYehuda which is very nicely explained:    • The Octagon In A Parallelogram   If you like my videos, you can support me at Patreon:   / mindyourdecisions   Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you. My Blog: http://mindyourdecisions.com/blog/ Twitter:   / preshtalwalkar   Facebook:   / 168446714965   Google+: https://plus.google.com/1083366085665... Pinterest:   / preshtalwalkar   Tumblr:   / preshtalwalkar   Instagram:   / preshtalwalkar   Patreon:   / mindyourdecisions   Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r My Books "The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.8/5 stars on 30 reviews) https://www.amazon.com/gp/product/150... "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 2 reviews) https://www.amazon.com/gp/product/152... "Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews. https://www.amazon.com/gp/product/151... "Math Puzzles Volume 2" is a sequel book with more great problems. (rated 5/5 stars on 3 reviews) https://www.amazon.com/gp/product/151... "Math Puzzles Volume 3" is the third in the series. (rated 3.8/5 stars on 4 reviews) https://www.amazon.com/gp/product/151... "40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.3/5 stars on 12 reviews) https://www.amazon.com/gp/product/151... "The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 4 reviews) https://www.amazon.com/gp/product/150... "Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 3 reviews) https://www.amazon.com/gp/product/150...