A circle is inscribed in a right triangle with legs 6 cm and 8 cm and hypotenuse 10 cm. Find its radius.

The tangent lengths from the right-angle vertex both equal $r$. So $(6-r)+(8-r)=10$, giving $r=2$ cm. (Shortcut: $r=\frac{a+b-c}{2}$.) 2.4 cm is the altitude to the hypotenuse divided by 2, not the inradius.