CAT (QA) PYQs

ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of in circle of $\triangle$ADE is

In a triangle ABC, $\angle BCA = 50^\circ$. D and E are points on AB and AC, respectively, such that AD = DE. If F is a point on BC such that BD = DF, then $\angle FDE$, in degrees, is equal to

A triangle ABC is formed with AB = AC = 50 cm and BC = 80 cm. Then, the sum of the lengths, in cm, of all three altitudes of the triangle ABC is