Project ForgeGeneral Aptitude
Quantitative Aptitude
GATE 2022
Medium
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/sqrt(2)
- B1/(2*sqrt(2))
- Csqrt(2)
- D2*sqrt(2)
Explanation
Joining the midpoints of a unit square's sides produces a smaller SQUARE (a special rhombus) with both diagonals equal to 1 (the distance between midpoints of opposite sides). Its side length is 1/sqrt(2) (diagonal/sqrt(2)). The largest inscribed circle in a square has diameter equal to the square's side, so diameter = 1/sqrt(2).
Source: GATE ME 2022 Session 1 (ME-1) (2022)
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