21 Sept 2013

Prize Maths Quiz: Inscribed Hexagon Puzzle (PMQ37)


The figure ABCDEF is a cyclic hexagon with lengths AB = CD = EF = 5, BC = DE = 2 and AF = 11. Given that the area of the hexagon is 54, find the rational value of the length BE.




As usual, assume this is a competition question. You have an ample supply of paper and pens and... that's it! Of course, this isn't a timed competition so that finding the answer is not so hard, but the important thing is to have a good solution method that can also be used in the future. Enjoy!






IMPORTANT CHANGES TO THE PRIZE MATHS QUIZ!

YOU MAY NOW DISCUSS THIS PMQ PROBLEM IN THE COMMENTS BELOW AND GIVE YOUR ANSWERS AND SOLUTION METHOD.

I HOPE THIS WILL MAKE THE COMMENTS MORE VIBRANT!

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How to Enter

IF YOU ARE A STUDENT, you may still send your complete solution by email to pmq33bernoulli@giftedmaths.com.[note that this email still works] This email address shall be removed after the competition closes to avoid spam. This PMQ37 competition closes on WEDNESDAY 25 SEPTEMBER at 23:59 GMT. 

The Prize

The prizes for this PMQ are 3 free places in our Online Maths Club for ONE YEAR. The very first correct solution will receive a prize plus two others randomly selected from all the other correct answers. The email time stamp shall determine the order of entries received. All winners can have their name posted and a link to their own online profile at their favourite social network or their own blog.

Quick Rules

Look at the expanded rules on our PMQ page.
Anybody can enter our Prize Maths Quiz; adults and students.
Use the official server clock in the right column to avoid late entries.
All emails and email addresses sent to us will be deleted after the winners have been processed.
DO NOT submit your entries to the comments section at the bottom of this post.
You CAN discuss it there but you must email us to enter the competition.
We adhere to COPPA guidelines regarding children's online safety and security.
Enjoy the challenge!
Send us your solution! You can't win if you don't participate.
Then tell your friends!

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