The orthocentre of the triangle formed by the points $(1,3), (-3,5)$ and $(5,-1)$ is

If the orthocentre of the triangle formed by the lines $2x+3y-1=0$,$x+2y-1=0$,and $ax+by-1=0$ is the centroid of another triangle,whose circumcentre and orthocentre are $(3,4)$ and $(-6,-8)$ respectively,then the value of $|a-b|$ is..........

If the coordinates of the vertices of triangle $ABC$ are $(6, 0)$,$(0, 6)$,and $(7, 7)$ respectively,find the circumcenter of the triangle.

For a triangle formed by the vertices $(0,0)$,$(4,0)$,and $(3,4)$,the orthocenter is:

Find the incenter of the triangle with vertices $(1, \sqrt{3})$,$(0, 0)$,and $(2, 0)$.

$A$ tower stands vertically inside an acute-angled triangular park $\Delta PQR$. If the angle of elevation of the top of the tower from each corner of the park is the same,then in $\Delta PQR$,the foot of the tower is at the