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 ? 

This question was previously asked in
CDS Elementary Mathematics 16 April 2023 Official Paper
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  1. 4 cm 
  2. 6 cm 
  3. 8 cm 
  4. 16 cm 

Answer (Detailed Solution Below)

Option 3 : 8 cm 
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Detailed Solution

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Formula used:

Area of equilateral triangle = (√3/4) (side)2

Calculation:

F2 Savita Defence 31-5-23 Sachin K D24

OA = OB = OC = radius (r)

Since OABC is a rhombus

BC = AB = r

Therefore, ΔOAB & ΔOBC are equilateral trainge 

According to the question

Area of rhombus = 32√3

Area of ΔOAB + Area of ΔOBC = 32√3

(√3/4)r2 + (√3/4)r2 = 32√3

2 [(√3/4) × r2] = 32√3

r2 = 64

r = 8 cm

∴ The radius of the circle is 8 cm2

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