The incentre of the triangle formed by the vertices $(0, 0)$,$(5, 12)$,and $(16, 12)$ is:

The orthocentre of a $\Delta ABC$ is $B$ and the circumcentre is $S(a, b)$. If $A$ is the origin,then the coordinates of $C$ are-

If the equations of the perpendicular bisectors of the sides $AB$ and $AC$ of a $\triangle ABC$ are $x-y+5=0$ and $x+2y=0$ respectively,and if $A$ is $(1,-2)$,then the equation of the perpendicular bisector of the side $BC$ is

If $\left( \frac{3}{2}, 0 \right)$,$\left( \frac{3}{2}, 6 \right)$,and $(-1, 6)$ are the midpoints of the sides of a triangle,find the incenter of the triangle.

Two vertices of a triangle are $(4, -3)$ and $(-2, 5)$. If the orthocentre of the triangle is at $(1, 2)$,then the third vertex is

Show that the area of the triangle formed by the lines $y=m_{1}x+c_{1}$,$y=m_{2}x+c_{2}$ and $x=0$ is $\frac{(c_{1}-c_{2})^{2}}{2|m_{1}-m_{2}|}$.