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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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Solution metasolution | Comment 1 of 3
A regular hexagon fits the description, so if there's a unique solution that doesn't depend on other, nonspecified, conditions, the answer is 1, as all the sides are equal in length in the regular hexagon.

The regular hexagon might be the only one that fits the description; in that case it's proved. If not, then only the assumption that all cases would have the same result allows us to say the answer is 1.

  Posted by Charlie on 2015-09-01 09:59:46
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