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GATE 2021 ME (ME2) – Question 8

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

The ratio of the area of the inscribed circle to the area of the circumscribed circle of an equilateral triangle is

Equilateral triangle with its inscribed and circumscribed circles. See the attached source image.
  1. $1/8$
  2. $1/6$
  3. $1/4$
  4. $1/2$

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Correct answer: (C) $1/4$

Explanation

For an equilateral triangle, inradius r is one-third of the altitude and circumradius R is two-thirds, so R=2 r.

Circle areas scale as radius squared. Thus $A_i/A_c=(r/R)^2=\mathbf{1/4}$, **C**.