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Question
OABC is a rhombus whose three vertices A, B and C lie on a circle with centre O. If the area of the rhombus is `32sqrt(3) cm^2` find the radius of the circle.
Solution
Area of rhombus = `32sqrt(3) cm^2`
But area of rhombus OABC = 2 × area of ΔOAB
Area of rhombus OABC = `2 xx sqrt(3)/4 r^2`
Where r is the side of the equilateral triangle OAB.
`2 xx sqrt(3)/4 r^2 = 32sqrt(3)`
`=> sqrt(3)/2 r^2 = 32sqrt(3)`
`=>` r2 = 64
`=>` r = 8
Therefore, radius of the circle = 8 cm
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