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GATE 2022 ME (ME1) – Question 7

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

A rhombus is formed by joining the midpoints of the sides of a unit square. What is the diameter of the largest circle that can be inscribed within the rhombus?

  1. $\frac{1}{\sqrt{2}}$
  2. $\frac{1}{2\sqrt{2}}$
  3. $\sqrt{2}$
  4. $2\sqrt{2}$

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Show answer and explanation

Correct answer: (A) $\frac{1}{\sqrt{2}}$

Explanation

The rhombus is a square of side $\frac{\sqrt{2}}{2}$ (its diagonals are 1 each). The largest inscribed circle has a diameter equal to the side: $\frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}$.