Altitude of a Triangle

Name the orthocentre of $△PQR$.

A square is drawn on the altitude of an equilateral triangle of sides $2$ metres. If the altitude of the square is $\sqrt{k} \mathrm{m}$, then find the value of $k$.

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

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

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

The altitudes of a triangle intersect at _____.

The area of a circle inscribed in an equilateral triangle is $36\mathrm{\pi }$ $sq units$. The length of altitude of triangle is:

Draw all three altitudes for the following triangles and explain how they are different:

$G$ is the centroid of the equilateral $∆ABC$. If $AB=10 cm$, then length of the $AG$ is :