OABC is a rhombus whose three vertices lie on a circle with centre at O. If the area of the rhombus is 32\sqrt{3} square cm, then what is the radius of the circle?

Explanation

Vertices A, B, C lie on the circle with center O, so OA = OB = OC = r. Since OABC is a rhombus, OA = AB and OC = BC. Therefore, triangles OAB and OCB are equilateral triangles with side r. Area of rhombus = 2 \times (\frac{\sqrt{3}}{4}r^2) = \frac{\sqrt{3}}{2}r^2 = 32\sqrt{3}. This gives r^2 = 64 \implies r = 8 cm.

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