Quantitative Aptitude – Geometry – Circle – a circle is inscribed in a rhombus


Slot – 1 – Quantitative Aptitude – Geometry – Circle – a circle is inscribed in a rhombus


Q. A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of the circle to the area of rhombus is?
  1. 6π/25
  2. 3π/25
  3. 2π/15
  4. 5π/18

Answer: 6π/25

Solutions:
a circle is inscribed
Area of rhombus=12*16/2 = 96
Let h=radius ; a=diagonal1; b=diagonal2
a=12
b=16
AB^2=(a/2)^2 + (b/2)^2=6^2+8^2 = 36+64= 100
AB=10
(a/2*b/2)/2=AB*h/2
6*8=10*h
H=4.8
Area of circle=Pi*4.8*4.8
Ratio of areas = Pi*4.8*4.8/96
On solving= Pi*6/25


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