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GATE 2021 ME (ME1) – Question 3

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

In the above figure, O is the center of the circle and, M and N lie on the circle. The area of the right triangle MON is 50 cm². What is the area of the circle in cm² ?

Circle centred at O with perpendicular radii OM and ON forming a right triangle. See the attached source image.
  1. $2\pi$
  2. $50\pi$
  3. $75\pi$
  4. $100\pi$

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Show answer and explanation

Correct answer: (D) $100\pi$

Explanation

OM and ON are perpendicular radii, each of length r. Thus triangle area is $r^2/2=50$, giving r²=100.

Circle area is $\pi r^2=\mathbf{100\pi}$ cm², **D**.