Find the area of a right-angled triangle, the radius of whose circumcircle measure 8 cm and the altitude drawn to the hypotenuse measures 6 cm.

Radius of circle $=8cm$ and
Altitude $=6cm$
Since, in a right-angled triangle the hypotenuse is the diameter of circumcircle. (given)
This implies,
Hypotenuse $=2$(Radius)
                      $=2\times 8$
                      $=16$
$\Rightarrow$ Hypotenuse $=16cm$

Area of a triangle $=\frac{1}{2}\times Base\times Height$
(Consider hypotenuse as base and the altitude to the hypotenuse as height)
                              $=\frac{1}{2}\times 16\times 6$
                              $=48$
$\Rightarrow$ Area of a triangle $=48c{m}^2$