#### Question

OABC is a rhombus whose three vertices A, B and C lie on a circle with centre O.

(ii) If the area of the rhombus is 32 3 cm2 find the radius of the circle.

#### Solution

Area of rhombus = `32 sqrt(3) cm ^2`

But area of rhombus OABC = `2xx ` area of ΔOAB .

Area of rhombus OABC = `2xx 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)`

⇒ `r^2 = 64`

⇒ r= 8

Therefore, radius of the circle = 8 cm

Is there an error in this question or solution?

Solution Oabc is a Rhombus Whose Three Vertices A, B and C Lie on a Circle with Centre O. (Ii) If the Area of the Rhombus is 32 3 Cm2 Find the Radius of the Circle. Concept: Chord Properties - Equal Chords Are Equidistant from the Center.