Question

A rhombus OABC is drawn inside a circle whose centre is at O in such a way that the vertices A, B and C of the rhombus are on the circle. If the area of the rhombus is 32√3 m², then the radius of the circle is

(a) 64 m 

(b) 8 m 

(c) 32 m 

(d) 46 m

Answer 1

(b) 8 m.

Let AC = 2x, OB = 2y. 

∴ Radius = OC = 2y = OB

From Δ ODC, 

OC² = OD² + CD² 

⇒ 4y² = y² + x² ⇒ x² = 3y² ⇒ x = √3 y    … (1) 

Also, 

Area of Δ ODC = \(\frac12\) × Area of rhombus OABC

⇒ \(\frac{1}{2}\times{x}\times{y}\) = \(\frac14\) x 32√3 ⇒ xy = 16√3 ......(2)

From (1) and (2) we have, y = 4 and x = 4√3 

∴ Radius of the circle = 2y = 8 m.