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

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Math Expert
Joined: 02 Sep 2009
Posts: 46167
If the circle above has a radius of 4, what is the perimeter of the in [#permalink]

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18 Jan 2018, 03:07
00:00

Difficulty:

45% (medium)

Question Stats:

74% (01:16) correct 26% (02:04) wrong based on 31 sessions

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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 [ 13.57 KiB | Viewed 387 times ]

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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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18 Jan 2018, 06:29
Bunuel wrote:

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

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If the circle above has a radius of 4, what is the perimeter of the in   [#permalink] 18 Jan 2018, 06:29
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