[ Inscribed Quadrilaterals ] $[$ Midline of a Trapezoid ]

A circle is inscribed in an isosceles trapezoid with an angle of $30^{\circ}$. Its midline is equal to 10. Find the radius of the circle.
The sum of the bases is equal to twice the midline, i.e., 20. The sum of the lateral sides is equal to the sum of the bases. Therefore, the lateral side of the trapezoid is 10, and the height of the trapezoid is half of the lateral side, i.e., 5.

Therefore, the radius of the inscribed circle is 2.5.

## Answer

$2.5$.