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Convex cyclic hexagon $ABCDEF$. Prove $AC \cdot BD \cdot CE \cdot DF \cdot AE \cdot BF \geq 27 AB \cdot BC \cdot CD \cdot DE \cdot EF \cdot FA$
Convex hexagon $ABCDEF$ inscribed within a circle. Prove that
$$AC \cdot BD \cdot CE \cdot DF \cdot AE \cdot BF \geq 27 AB \cdot BC \cdot CD \cdot DE \cdot EF \cdot FA\,.$$
I was thinking of ...
- 755
0
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0
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For convex cyclic hexagon $ABCDEF$, show $AC\cdot BD \cdot CE \cdot DF \cdot EA\cdot FB \geq 27\cdot AB\cdot BC\cdot CD \cdot DE\cdot EF\cdot FA$ [duplicate]
Given a convex hexagon $ABCDEF$ inscribed in the circle, prove that
$$AC\cdot BD \cdot CE \cdot DF \cdot EA\cdot FB \;\geq\; 27\cdot AB\cdot BC\cdot CD \cdot DE\cdot EF\cdot FA$$
("$AC$" means the ...
user740859
13
votes
2
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Polygons with 2 diagonals of fixed length (part two)
In this question of mine
Polygons with two diagonals of fixed length
I've presented the following particular polygon $P$
and I've asked the following question: is it possible to shorten one or ...
user372511
1
vote
3
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2k
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Area of a cyclic polygon maximum when it is a regular polygon
My question: Let $n$ points $A_1, A_2,\ldots,A_n$ lie on given circle then show that $\operatorname{Area}(A_1A_2\cdots A_n)$ maximum when $A_1A_2\cdots A_n$ is an $n$-regular polygon.
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