perplexus.info :: Shapes : Convex Hexagon and Ratio Product

Convex Hexagon and Ratio Product (Posted on 2015-09-01)

PQRSTU is a convex hexagon such that:

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

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

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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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