A square is inscribed in a circle. And an equilateral triangle of side 4√3 cm is inscribed in that square. What will be the length of the diagonal of a square?
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The radius of the circle is equal to the distancd between the corner of the triangle and the centre of the triangle. This distance is equal to 2/3 of the total altitude of the triangle(A mathematical fact.)
Altitude = Side × 3^0.5 ÷ 2
Altitude = 4 × 3 ÷ 2
Altitude = 6 cm.
Radius = Altitude × 2 ÷ 3
Radius = 6 × 2 ÷ 3
Radius = 4 cm
Diameter = 2 × Radius
Diameter = 2 × 4
Diameter = 8 cm
Diameter = Length of Side of the Square = 8 cm
Diagonal of the Square = (Side^2 + Side^2)^0.5 (By Pythagoras Theorem)
Diagonal of the Square = 8 × 2^0.5 cm.
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Altitude = Side × 3^0.5 ÷ 2
Altitude = 4 × 3 ÷ 2
Altitude = 6 cm.
Radius = Altitude × 2 ÷ 3
Radius = 6 × 2 ÷ 3
Radius = 4 cm
Diameter = 2 × Radius
Diameter = 2 × 4
Diameter = 8 cm
Diameter = Length of Side of the Square = 8 cm
Diagonal of the Square = (Side^2 + Side^2)^0.5 (By Pythagoras Theorem)
Diagonal of the Square = 8 × 2^0.5 cm.
I hope it helps you...
mark as brainliest
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