CAT (QA) PYQs

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

From a triangle $ABC$ with sides of lengths $40$ ft, $25$ ft and $35$ ft, a triangular portion $GBC$ is cut off where $G$ is the centroid of $ABC$. The area, in sq ft, of the remaining portion of triangle $ABC$ 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