An equilateral triangle is inscribed in a circle. If the

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An equilateral triangle is inscribed in a circle. If the [#permalink]

11 Apr 2012, 07:58

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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?

A) 9z²-pi*y=0
B) 3z²-pi*y=0
C) pi*z²-3y=0
D) pi*z²-9y=0
E) pi*z²-27y=0

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Re: An equilateral triangle is inscribed in a circle. If the [#permalink]

11 Apr 2012, 08:20

BN1989 wrote:

We need to establish a relationship between the perimeter of the triangle and the area of the circle.

The radius of the circumscribed circle is R=a\frac{\sqrt{3}}{3}, where a is the side of the inscribed equilateral triangle (check this for more: math-triangles-87197.html).

Now, the area of the circle is \pi{r^2}=\pi{\frac{a^2}{3}}=y and the perimeter of the triangle is 3a=z. Now, you can plug these values in answer choices to see which is correct.

Option E fits: \pi{z^2}-27y=9a^2\pi-9a^2\pi=0.

Answer: E.
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Re: An equilateral triangle is inscribed in a circle. If the [#permalink] 11 Apr 2012, 08:20

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An equilateral triangle is inscribed in a circle. If the

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