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A regular hexagon (H1) of side 8 cm is inscribed in a circle(C1). Another circle(C2) is inscribed in the regular hexagon (H1) and it circumscribes another regular hexagon(H2) and so on. Find the sum of the areas of all such possible regular hexagons.
  • a)
    384√3
  • b)
    288√3
  • c)
    192√3
  • d)
    96√3
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A regular hexagon (H1) of side 8 cm is inscribed in a circle(C1). Anot...

Radius of C1  = 8
Side of the regular hexagon(H2) = radius of the circle(C2) = the perpendicular distance from the centre to the base of the hexagon, which is the height of the equilateral triangle whose side is 8.
Hence, the side of the nth hexagon is √3/2 times the side of the (n-1)th hexagon.
Hence the required sum

This is in GP with the first term as  and common ratio 3/4.
Sum to infinite terms of the GP
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A regular hexagon (H1) of side 8 cm is inscribed in a circle(C1). Another circle(C2) is inscribed in the regular hexagon (H1) and it circumscribes another regular hexagon(H2) and so on. Find the sum of the areas of all such possible regular hexagons.a)384√3b)288√3c)192√3d)96√3Correct answer is option 'A'. Can you explain this answer?
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