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let ABCDEF be a convex hexagon in which the diagonals AD,BE,CF aew concurrent at O. Suppose the area of the triangle OAF is the geometric mean of those of OAB and OEF; the area of the triangle OBC is the geometric mean of those of OAB and OCD. Prove that the area of the triangle OED is the goemetric mean of those of OCD and OEF

let ABCDEF be a convex hexagon in which the diagonals AD,BE,CF aew concurrent at O.  Suppose the area of the triangle OAF is the geometric mean of those of OAB and OEF;  the area of the triangle OBC is the geometric mean of those of OAB and OCD. Prove that the area of the triangle OED is the goemetric mean of those of OCD and OEF

Grade:12

2 Answers

Fawz Naim
37 Points
11 years ago

In a hexagon all the angles are of 120 degree and if we join all the opposite vertices then six equilateral triangles are formed as they are in the figure so the square of the area of any triangle is equal to the product of any two other triangles. Hence the proof given above is verified.2210_22392_hexagon.jpeg

Sudheesh Singanamalla
114 Points
11 years ago

can Some one please redo this for me !

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