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.

Answer 1

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