In the 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 cm^2. What is the area of the circle in cm^2?
A. 2pi B. 50pi C. 75pi D. 100pi
GATE 2021 · General Aptitude · Triangles · medium
Answer: Area of the circle = 100pi cm^2.
Identify the two legs of the right triangle: Since O is the center and M, N lie on the circle, OM = ON = r. The right angle is at O, so the two legs are OM and ON.
Apply triangle area formula to get r^2: 50 = (1/2) * r * r = r^2 / 2. Therefore r^2 = 100.
Compute area of the circle: Area_circle = pi * 100 = 100*pi cm^2.