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If the circle above has a radius of 4, what is the perimeter of the in

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If the circle above has a radius of 4, what is the perimeter of the in  [#permalink]

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New post 18 Jan 2018, 03:07
1
4
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

72% (02:01) correct 28% (02:41) wrong based on 81 sessions

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If the circle above has a radius of 4, what is the perimeter of the in  [#permalink]

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New post 18 Jan 2018, 06:29
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Bunuel wrote:
Image
If the circle above has a radius of 4, what is the perimeter of the inscribed equilateral triangle?

A. \(6\sqrt{2}\)

B. \(6\sqrt{3}\)

C. \(12\sqrt{2}\)

D. \(12\sqrt{3}\)

E. 24

Attachment:
The attachment 2018-01-18_1405.png is no longer available


As we can see the left bottom corner of the triangle becomes a 30º-60º-90º triangle where the hypotenuse of the triangle is same as Radius i.e. 4

i.e. Half of the side of the equilateral triangle is the side opposite to 60º in 30º-60º-90º triangle

hence Half of the side of equilateral triangle = 2√3

i.e. Side of the Equilateral triangle = 4√3

ie. Perimeter of the triangle = 3*4√3 = 12√3

ANswer: option D
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Re: If the circle above has a radius of 4, what is the perimeter of the in  [#permalink]

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New post 30 Jun 2019, 07:33
Bunuel wrote:
Image
If the circle above has a radius of 4, what is the perimeter of the inscribed equilateral triangle?

A. \(6\sqrt{2}\)

B. \(6\sqrt{3}\)

C. \(12\sqrt{2}\)

D. \(12\sqrt{3}\)

E. 24

Attachment:
2018-01-18_1405.png


If we draw a perpendicular from the centre to all the side and also join all the vertices to the centre we will get 6 right angled triangle which is 30-90-60

hypotenuse=radius=4
and side opp 60 degree=\sqrt{3}/2 *hypotenuse=2\sqrt{3}

hence one side is 4\sqrt{3} and perimeter 3* 4\sqrt{3}=12\sqrt{3}
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If the circle above has a radius of 4, what is the perimeter of the in  [#permalink]

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New post 11 Jul 2019, 05:07
Radius of circumscribed circle of an equilateral triangle is, R= (A/√3), where A is length of a side of equilateral triangle and R is radius of circumscribed circle.
Here, 4= (A/√3), A= 4√3, perimeter= 12√3. Answer is Option D.

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Re: If the circle above has a radius of 4, what is the perimeter of the in  [#permalink]

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New post 11 Jul 2019, 07:16
Radii of circle outscribed of equilateral triangle: R={ a*sqrt(3) } / 3. Hence, a = R*sqrt(3) ; Perimetr = 3*R*sqrt(3) =3*4*sqrt(3)=12*sqrt(3)
( Radii of circle inscribed in quilateral triangle: R= { a*sqrt(3) } / 6 )
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Re: If the circle above has a radius of 4, what is the perimeter of the in   [#permalink] 11 Jul 2019, 07:16
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