CAT (QA) PYQs

Let $P$ be an interior point of a right-angled isosceles triangle $ABC$ with hypotenuse $AB$ . If the perpendicular distance of P from each of $A B, B C$, and $C A$ is $4(\sqrt{2}-1) \mathrm{cm}$, then the area, in sq cm, of the triangle $A B C$ is

A circle of diameter $8$ inches is inscribed in a triangle ABC where $\angle A B C=90^{\circ}$. If $B C=10$ inches then the area of the triangle in square inches is

Let $T$ be the triangle formed by the straight line $3x + 5y - 45 = 0$ and the coordinate axes. Let the circumcircle of $T$ have radius of length $L,$ measured in the same unit as the coordinate axes. Then, the integer closest to $L$ is