Altitude of a Triangle

Name the orthocentre of $△PQR$.

$△ABC$ is a right angled triangle. If $CD=k \mathrm{cm}$ then find $k$.

If the altitude to side $AC$ of triangle with side $AB = 20 \mathrm{cm}, AC = 20 \mathrm{cm}, BC = 30 \mathrm{cm}$ is $7.5\sqrt{k }\mathrm{cm}$ then find $k$.

If the altitude of a triangle is $k \mathrm{cm}$, its area is $120 {\mathrm{cm}}^2$ and its base is $6 \mathrm{cm}$ then find $k$.

If the altitude of an equilateral triangle when its equal sides are given as $10 \mathrm{cm}$ is $k\sqrt{3} \mathrm{cm}$ then find $k$.

Every triangle has $4$ altitudes, one from each vertex.

The orthocenter is located inside the triangle in _____ triangle. (Acute/Right) 

Given: $BX$ is the altitude, $\angle BAX=40°$. If $\angle 1=k°$ then find $k$.

Given: $AX$ is the altitude, $\angle CAB\cong \angle B, \angle C=50°$. If $\angle B$ is $k°$ then find $k$

The perpendicular from the vertex of a triangle to the side is called _____ of the triangle.

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 _____.

In the equilateral triangle $\mathrm{A}\mathrm{B}\mathrm{C}$, the three altitudes $\mathrm{A}\mathrm{L}$, $\mathrm{B}\mathrm{M}$, $\mathrm{C}\mathrm{N}$ have been drawn that intersect at $\mathrm{O}$.
$\mathrm{B}\mathrm{O}=\mathrm{C}\mathrm{O}$

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 :