Concurrent Lines in Triangles

The excentre is defined as:

The point of two external angle bisector for any side of a triangle and internal angle bisector of the angle opposite side chosen is called 

The incentre is defined as:

The point of intersection of the bisectors of the angles of any triangle is called

The circumcentre is defined as:

The point of intersection of the perpendicular bisectors of the sides of a triangle is called:

In an obtuse - angled triangle, the obtuse angled is $110°$. Find the angle made on its orthocentre.

If the coordinates of the mid-points of the sides of a triangle are $\left(5,2\right), (3,3)$ and $\left(2,2\right)$. Find its centroid.

Name the triangle for which centroid, circumcentre, orthocentre and incentre coincide with each other.

Where does the orthocentre lie in the case of an acute-angled triangle?

Where does the orthocentre lie in the case of an obtuse-angled triangle?

Where does the orthocentre lie in the case of a right angled triangle?

In triangle $PQR$, $PS$ is a median and $QS=3.5 \mathrm{cm}$ and $QR=k \mathrm{cm}$, find the value of $k$.

In figure, point $G$ is the point of concurrence of the medians of $△PQR$. If $GT=2.5$, find the lengths of $PT$.

In $△ABC,$ the median $AD, BE$ and $CF$ passes through the point $G$. If $GF=4 \mathrm{cm}$ then, find $GC$.

In $△ABC,$ the median $AD, BE$ and $CF$ passes through the point $G$. If $AD=7.5 \mathrm{cm},$ then find $GD$ (in $\mathrm{cm}$) (correct up to one decimal place)

Find in how many points do the three medians of a triangle meet.