CAT 2020 Question Paper | Quants Slot 1

CAT Previous Year Paper | CAT Quants Questions | Question 18

This question is from Geometry. It discusses about a circle that is inscribed in a rhombus. We need to find the ratio of the area of the circle to the area of the rhombus. Geometry is an important topic with lots of weightage in CAT exam. Make sure you master Geometry by practicing a lot of questions.

Question 18 : 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 the rhombus is

  1. \\frac{2π}{15})
  2. \\frac{6π}{25})
  3. \\frac{3π}{25})
  4. \\frac{5π}{18})

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Explanatory Answer

Diagonals of a rhombus are perpendicular bisectors of each other
If diagonals are 12 and 16
Half of diagonals are 6 and 8 third side will become 10 = side of rhombus
Radius of the circle will be perpendicular to the side of the rhombus
Because side of the rhombus is tangent to the circle
The triangle is taken by half a diagonal (6) and (8) from the original figure
triangle
rhombus
Just equating the areas
\\frac{1}{2}) × 8 × 6 = \\frac{1}{2}) × 10 × h
h = \\frac{24}{5}) = same as radius of the circle (r)
Now, area of circle : area of rhombus
π × \\frac{24}{5}) × \\frac{24}{5}) : \\frac{1}{2}) × 12 × 16
6π : 25


The question is "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 the rhombus is"

Hence, the answer is, "\\frac{6π}{25})"

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