Let the midpoints of the sides of a triangle $ABC$ be $(\frac{5}{2}, 7)$,$(\frac{5}{2}, 3)$,and $(4, 5)$. If its incentre is $(h, k)$,then $3h + k$ is equal to:

The equations of the sides of a triangle are $x - 2y = 0$,$4x + 3y = 5$,and $2x + y = 0$. Through which point does the line $3y - 4x = 0$ pass?

$A$ vertex of an equilateral triangle is $(2, 3)$ and the equation of the opposite side is $x + y = 2$. Then,the equation of one of the other two sides is:

The incenter of an equilateral triangle is $(-6, 5)$ and one of its sides lies on the $y$-axis. Find the length of the side of the triangle.

$A$ triangle is formed by the $Y$-axis,the straight line $L$ passing through the points $(3,0)$ and $(1, 4/3)$,and the straight line perpendicular to the line $L$ and passing through the point $(8,1)$. The area of the triangle (in sq units) is

In the figure given below,$ABCDEF$ is a regular hexagon of side length $1$,$AFPS$ and $ABQR$ are squares. Then,the ratio $\frac{\operatorname{ar}(APQ)}{\operatorname{ar}(SRP)}$ equals