1. **Problem statement:** We have an isosceles trapezoid with parallel sides (bases) of lengths 8 units and 18 units, and a circle inscribed inside it. We need to find the radius of the inscribed circle. 2. **Key property:** For a trapezoid to have an inscribed circle, it must be tangential, meaning the sum of the lengths of the non-parallel sides (legs) equals the sum of the lengths of the parallel sides (bases). Since the trapezoid is isosceles, both legs are equal in length. Let each leg be $x$. 3. **Using the tangential trapezoid property:** $$ 2x = 8 + 18 = 26 \implies x = 13 $$ 4. **Height of the trapezoid:** Using the Pythagorean theorem, the height $h$ can be found by considering the right triangle formed by the leg, the height, and half the difference of the bases: $$ h = \sqrt{x^2 - \left(\frac{18 - 8}{2}\right)^2} = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12 $$ 5. **Radius of the inscribed circle:** The radius $r$ of the inscribed circle in a tangential trapezoid is given by: $$ r = \frac{h}{2} = \frac{12}{2} = 6 $$ **Final answer:** The radius of the inscribed circle is $6$ units.