The given triangle is a right-angled triangle with side lengths: 6 units, 8 units, and 10 units.
Since it's a right triangle, we can use the formula for the inradius \( r \) of a right-angled triangle:
\[ r = \frac{a + b - c}{2} \] where \( a \) and \( b \) are the legs, and \( c \) is the hypotenuse.
Substituting the values: \( a = 6 \), \( b = 8 \), and \( c = 10 \), we get:
\[ r = \frac{6 + 8 - 10}{2} = \frac{4}{2} = 2 \]
Therefore, the radius of the incircle is 2 units.