Three non-concentric circles of equal radii are drawn such that each circle touches the other two ex

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30 Oct 2015 Area

Three non-concentric circles of equal radii are drawn such that each circle touches the other two externally. The centres are joined to form a triangle whose area is 17320.5 cm^2. Find the area of the triangle not included in the circles.

OPtion

1) 1740.5 cm^2
2) 1650.5 cm^2
3) 1540.5 cm^2
4) 1690.5 cm^2
5) 1475.5 cm^2
6) 1620.5 cm^2
7) 1680.5 cm^2
8) 1850.5 cm^2
9) 1720.5 cm^2
10)None of these

Solution

Note that the triangle is equilateral and side length is twice radius of circle. Also from area of triangle we can obtain side length of the triangle and consequently, the radius of the circle, and its area.
solve it by using figure
Area of triangle not included in the circle
= Area of triangle - Area of sectors
= 1620.5 cm^2
Option 6)

Correct Option: 6 Best Solution (9)

Deepak kumar singh   9 years AGO

1.74/4*(2r)^2=17320.5 => r=100
area of circle inside triangle=3*(60/360*3.14*(100)^2=15700
Required area=17320.5-15700=1620.5 ans

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Abhisheak Kumar Missu   9 years AGO

diameter of circle=200cm
radius of circle=100cm
area of circle enscribed by triangle=1/2*22/7*100*100=15714cm2
Area of triangle not circle=1620.5

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RANJAN FADIA   9 years AGO

area of equilateral triangle = (root 3* side ^2 )/4
=> 17320.5 = (root 3 * 4*r^2)/4 { since side =2r , r is radius }

=> r^2 = 17320.5 /(root 3)

now, required area = (area of equilateral triangle) - 3*(area of arc made in circle)

=> area = 17320.5 - {3* (pi * r^2)/6}
[since area of arc = (angle * pi *r^2) 360 degree angle ]

=> area = 17320.5 - (pi*17320.5)/2* root 3 )
= 1620.04 cm^2...................... ans.

[take pi =3.14 ]

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Robert Yogenson   9 years AGO

not included circle area ==area of triangle -3(pie*R^2)*1/6
17320.5- 1/2(pie *17320.5/root3) =1620.5

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Amit kumar yadav   9 years AGO

using area of equilateral triangle (sqrt(3)*a*a)/4 we find side=200 using sector formula
given area -(60/360)*pie*a*a*3 =1620.5

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VICKY JAISWAL   9 years AGO

area of triangl is ?3*r^2
so r=100
area of sector is (angle/360)*?r^2
and total 3 sector so tatal area is15700
remaining area is 17320.5-15700=1620.5cm^2

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Nandkishor jaiswal   9 years AGO

given that area of triangle is 17320.5 cm^2
sqrt(3)/4*a^2=17320.5
so, a=200 cm
now r=200/2=100 cm
now area of circle that are lie into the triangle is
3*60/360*3.14*100*100=15700 cm^2
so area of triangle that are lie into the circle is=
17320.5-15700=1620.5 cm^2

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Sushant Kumar   9 years AGO

Let each side of the triangle be a cm. Then,
Area = 17320.5cm2
⇒ 3√4a2=17320.5 [sinceArea=3√4(side)2]
⇒ a2=17320.5×43√=17320.5×41.73205=40000
⇒ a = 200
Thus, radius of each circle is 100 cm.
Now, required area
= Area of Δ ABC – 3 ×(Area of a sector of angle 60º in a circle of 100 cm)
=[17320.5−3(60360×3.14×100×100)]cm2
=(17320.5−15700)cm2=1620.5cm2

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sumit kumar   9 years AGO

according to question an equilateral triangle will form.
so area of equilateral triangle is (?3/4)*side^3=17320.5 cm^2
after solving it we get a=200 cm(approx).
so radius of circle will be r=a/2=100 cm
now area of 3 sector of circle is s2= 3*(angle/360)*?r^2=15700 cm^2
our design answer is =17320.5-s2
i.e 1620.5 cm^2.
option 6

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