CAT (QA) PYQs

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

The length of each side of an equilateral triangle ABC is $3 \mathrm{~cm}$. Let D be a point on BC such that the area of triangle ADC is half the area of triangle $A B D$. Then the length of $A D$, in cm , is

The coordinates of the three vertices of a triangle are: $(1, 2)$, $(7, 2)$, and $(1, 10)$. Then the radius of the in circle of the triangle is