IIM-K (BMSAT) 2025 (QA) PYQs

In triangle $ABC, AB = AC = x, ∠ABC = \theta$ and the circumradius is equal to $y$. Then $\frac{x}{y}$ equals

Let ABC be an equilateral triangle, with each side of length $k$. If a circle is drawn with diameter AB, then the area of the portion of the triangle lying inside the circle is

The lengths of the sides of a triangle are $x, 21$ and $40$, where $x$ is the shortest side. A possible value of $x$ is: