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Hexagon Hinder (Posted on 2016-02-12) Difficulty: 3 of 5
PQRSTU is a regular hexagon
A,B,C,D,E and F are the respective midpoints of sides PQ, QR, RS, ST, TU and UP.
PB, QC, RD, SE, TF and UA bound a smaller regular hexagon.
The ratio of the area of the smaller hexagon to the area of PQRSTU is equal to x/y, where x and y are relatively prime positive integers.

Determine x and y

No Solution Yet Submitted by K Sengupta    
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Some Thoughts General solution Comment 2 of 2 |
Do the same thing with a regular n-gon.

The ratio of the smaller to the larger will be cos^2(180/n)

This is a rational number only for 3,4,6

  Posted by Jer on 2016-02-12 09:16:19
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