2023 · Q57
OABC is a rhombus whose three vertices lie on a circle with centre at O. If the area of the rhombus is 32√3 square cm, then what is the radius of the circle?
Elementary MathematicsQuadrilaterals and Polygons
- A4 cm
- B6 cm
- C8 cm
- D16 cm
Explanation
O is a vertex of the rhombus and A, B, C lie on the circle centred at O, so OA = OB = OC = r. Then OA = AB = OB = r makes the rhombus two equilateral triangles of side r. Its area 2·(√3/4)r² = 32√3 gives r² = 64, so r = 8 cm (C).