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17 Oct 2019, 17:14
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
62% (02:17) correct
38%
(02:23)
wrong
based on 71
sessions
History
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Not Attempted Yet
An equilateral triangle circumscribes all the 3 circles, each of radius 1cm. What is the the perimeter of the equilateral triangle?
A. \(3(\sqrt{3}-1)\)
B. \(6(\sqrt{3}-1)\)
C. \(3(\sqrt{3}+1)\)
D. \(6(\sqrt{3}+1)\)
D. 18
A. \(3(\sqrt{3}-1)\)
B. \(6(\sqrt{3}-1)\)
C. \(3(\sqrt{3}+1)\)
D. \(6(\sqrt{3}+1)\)
D. 18
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17 Oct 2019, 19:26
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nick1816
For finding area of an equilateral triangle, we require to know the sides..
Draw lines as shownn...
(I) now take \(\triangle AOB....\angle OAB=\angle A/2=\frac{60}{2}=30\).
Hence AOB is 30-60-90 triangle, so sides are \(1:\sqrt{3}:2\)...OB is opposite 1, so AB=\(\sqrt{3}\) as it is opposite 60`
(II) BC = sum of radius of two circles = 1+1=2
(III) CD=AB=\(\sqrt{3}\)
Side of triangle = \(2\sqrt{3}+2\)
Perimeter = 3*side = \(3*(2\sqrt{3}+2)=6(\sqrt{3}+1)\)
If you did not know the method, the choices should have helped..
Had you joined the centers of circles, you woould have got a perimeter of 2=2+2=6.
Whereas the perimeter of triangle circumscribing the circles has to be more than double, so nearly..
A and B are less than 5..eliminated
C is 3*2.7=8.1, still closer to 6.
D is 6*2.7=16.2..Yes
E is 18 yes maybe
Now when you are dealing with triangle, \(\sqrt{3}\) seems more appropriate as all choices contain that and it deals with 30-60-90 triangle
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14 Jul 2020, 03:48
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In an equilateral triangle of side x, if 3 circles of equal radii r are drawn touching each other, and touching the sides of the equilateral triangle, then the relation between the side and the radius is given as x = 2r (√3 + 1)
Here r = 1, therefore the side of the equilateral triangle, x = 2 * 1 (√3 + 1) = 2(√3 + 1)
Perimeter = 3 * x = 3 * 2(√3 + 1) = 6(√3 + 1)
Option D
Arun Kumar
Here r = 1, therefore the side of the equilateral triangle, x = 2 * 1 (√3 + 1) = 2(√3 + 1)
Perimeter = 3 * x = 3 * 2(√3 + 1) = 6(√3 + 1)
Option D
Arun Kumar
