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Convex Hexagon and Ratio Product (Posted on 2015-09-01) Difficulty: 3 of 5
PQRSTU is a convex hexagon such that:

∠ Q + ∠ S + ∠ U = 360o and:
(PQ/QR)(RS/ST)(TU/UP) = 1

Find: (QR/RP)(PT/TU)(US/SQ)

No Solution Yet Submitted by K Sengupta    
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Comments: ( Back to comment list | You must be logged in to post comments.)
re: metasolution | Comment 2 of 3 |
(In reply to metasolution by Charlie)

I little playing around with Geometer's Sketchpad:

The hexagon does not need to be regular to fit this description.
The ratio product does appear to always be 1 when the conditions are met.

Note: some of the lengths in the ratio product are not side lengths.

  Posted by Jer on 2015-09-01 12:39:27

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