The in-centre of the triangle formed by the lines $x=0, y=0$ and $3x+4y=12$ is

Let $ABCD$ be a quadrilateral such that there exists a point $E$ inside the quadrilateral satisfying $AE=BE=CE=DE$. Suppose $\angle DAB, \angle ABC, \angle BCD$ are in an arithmetic progression. Then the median of the set $\{\angle DAB, \angle ABC, \angle BCD\}$ is

Consider four triangles with side lengths $(5, 12, 9)$,$(5, 12, 11)$,$(5, 12, 13)$,and $(5, 12, 15)$. Among these,the triangle with the maximum area has sides:

One side of a square is inclined at an acute angle $\alpha$ with the positive $x-$axis,and one of its extremities is at the origin. If the remaining three vertices of the square lie above the $x-$axis and the side of a square is $4$,then the equation of the diagonal of the square which is not passing through the origin is

The vertices of a triangle are $(2, 1)$,$(5, 2)$ and $(4, 4)$. The lengths of the perpendiculars from these vertices to the opposite sides are

The coordinates of the vertices $P, Q, R$ and $S$ of a square $PQRS$ inscribed in the triangle $ABC$ with vertices $A \equiv (0, 0)$,$B \equiv (3, 0)$,and $C \equiv (2, 1)$,given that two of its vertices $P$ and $Q$ lie on the side $AB$,are respectively: