IPMAT Indore (MCQ) PYQs

In a right-angled triangle ABC, the hypotenuse AC is of length 13 cm. A line drawn connecting the midpoints D and E of sides AB and AC is found to be 6 cm in length. The length of BC is

Let $\triangle ABC$ be a triangle right-angled at $B$ with $AB = BC = 18$. The area of the largest rectangle that can be inscribed in this triangle and has $B$ as one of the vertices is:

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