$A$ vertical pole of length $6\, m$ casts a shadow $4\, m$ long on the ground and at the same time a tower casts a shadow $28\, m$ long. Find the height of the tower. (in $m$)

In the figure,$OA \cdot OB = OC \cdot OD$. Show that $\angle A = \angle C$ and $\angle B = \angle D$.

In the figure,$ABD$ is a triangle right-angled at $A$ and $AC \perp BD$. Show that $AD^{2} = BD \cdot CD$.

An aeroplane leaves an airport and flies due north at a speed of $1000\, km/h$. At the same time,another aeroplane leaves the same airport and flies due west at a speed of $1200\, km/h$. How far apart will be the two planes after $1 \frac{1}{2}$ hours?

$E$ and $F$ are points on the sides $PQ$ and $PR$ respectively of a $\Delta PQR$. For the following case,state whether $EF || QR$: $PE = 3.9 \ cm, EQ = 3 \ cm, PF = 3.6 \ cm$ and $FR = 2.4 \ cm$.

Sides $AB$ and $BC$ and median $AD$ of a triangle $ABC$ are respectively proportional to sides $PQ$ and $QR$ and median $PM$ of $\Delta PQR$ (see Figure). Show that $\Delta ABC \sim \Delta PQR$.