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An equilateral triangle is inscribed in a circle. If the perimeter of
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06 Sep 2021, 10:00
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An equilateral triangle is inscribed in a circle. If the perimeter of the triangle is z inches and the area of the circle is y square inches, which of the following equations must be true?
An equilateral triangle is inscribed in a circle. If the perimeter of
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30 Nov 2021, 06:25
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Side of an equilateral triangle (a) inscribed in a circle with radius r is given by a = rโ๐ [ Watch this video to know how ]
=> Perimeter of triangle = 3a = 3 * โ๐ r = z (given) => r = \(\frac{z }{ 3 โ๐}\)
Area of circle with radius r = \(\pi r^2\) = y (given) => \(\pi\) * \((\frac{z }{ 3 โ๐})^2\) = y (substituting value of r from (1) ) => \(\pi\) * \(\frac{z^2}{9*3}\) = y => \(\pi\) * \(\frac{z^2}{27}\) = y => \(\pi\) * \(z^2\) = 27 * y => \(\pi z^2-27y=0\)
So, Answer will be E Hope it helps!
Watch the following video to Learn Properties of Equilateral Triangle inscribed in a Circle
Re: An equilateral triangle is inscribed in a circle. If the perimeter of
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06 Sep 2021, 17:42
3
Answer is E) pi *z^2โ27y=0
Let s be the side of the triangle and r be the radius of the circle, the relation between them is s = r * sqrt(3). So z = 3 * s = 3*sqrt(3) * r. and area = pi * r^2. All the answer choices are relation between y and z and y already has a pi in it, so in the answer only C,D,E has pi multiplied for z. Next step is simple, relation between z and y in terms of r and E is the only one that satisfies.
PS: Not sure this is the GRE method, please share if there is a shorter approach.
Re: An equilateral triangle is inscribed in a circle. If the perimeter of
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14 Apr 2024, 10:39
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Re: An equilateral triangle is inscribed in a circle. If the perimeter of [#permalink]