    Question

# A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3, 4 and 5 units. Then area of the triangle is equal to

A
93(1+3)π2
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B
93(31)π2
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C
93(1+3)2π2
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D
93(31)2π2
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Solution

## The correct option is A 9√3(1+√3)π2Circumference =3+4+5=2πr ⟹r=6π The arcs subtend angles that are proportionate to their lengths. i.e. 3θ,4θ,5θ 3θ+4θ+5θ=360∘ θ=30∘ ⟹ The 3 triangles subtend 90,120,150 angles. Area is given by 12absinC Total Area =12r2sinθ1+12r2sinθ2+12r2sinθ3 =12×36π2(1+√32+12) =9π2(3+√3)  Suggest Corrections  0      Similar questions
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