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.
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edge of triangle=2 radius
area of triangle=17320.5 cm^2
therefore area of triangle=3^(1/2)/4*a^2
17320.5cm^2=3^(1/2)/4*a^2
173205/10*4/3^(1/2)cm^2=a^2
a=194.14cm
a=2r
194.14 cm=2r
r=97.07cm
area of three sectors=3*60/360*22/7*97.07*97.07 cm^2
=14806.92 cm^2
area of triangle not included in the circles=area of triangle -area of three sectors
=(17320.5-14806.9)cm^2
2513.6 cm^2
area of triangle=17320.5 cm^2
therefore area of triangle=3^(1/2)/4*a^2
17320.5cm^2=3^(1/2)/4*a^2
173205/10*4/3^(1/2)cm^2=a^2
a=194.14cm
a=2r
194.14 cm=2r
r=97.07cm
area of three sectors=3*60/360*22/7*97.07*97.07 cm^2
=14806.92 cm^2
area of triangle not included in the circles=area of triangle -area of three sectors
=(17320.5-14806.9)cm^2
2513.6 cm^2
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