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An equilateral triangle is inscribed in a circle. How many times great

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An equilateral triangle is inscribed in a circle. How many times great  [#permalink]

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New post 31 Oct 2018, 01:00
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

56% (01:28) correct 44% (02:08) wrong based on 26 sessions

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An equilateral triangle is inscribed in a circle. How many times greater is the area of the circle than the area of the triangle?

A. π/√3

B. 3π/4

C. 4π/(3√3)

D. 3

E. 2π/√3

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Re: An equilateral triangle is inscribed in a circle. How many times great  [#permalink]

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New post 31 Oct 2018, 05:56
1
See diagram below, O divides PQ in 2:1 ratio (property of equilateral triangle)
PO = r, PQ = r + r/2 = 3r/2
Area of equilateral triangle = \(\sqrt{3}\)*\(a^2\)/4

Perpendicular bisector of a side has length \(\sqrt{3}\)*a/2 = PQ

Hence, 3r/2 = \(\sqrt{3}\)*a/2 which gives r = a/\(\sqrt{3}\)

Hence area of circle = pi*\(a^2\)/3

Ratio = (pi*\(a^2\)/3)/(\(\sqrt{3}\)*\(a^2\)/4) = 4*pi/3\(\sqrt{3}\)

Hence Option C
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Re: An equilateral triangle is inscribed in a circle. How many times great &nbs [#permalink] 31 Oct 2018, 05:56
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