In an isosceles trapezoid, the angle at the base is $50^{\circ}$, and the angle between the diagonals, facing the lateral side, is $40^{\circ}$. Is the center of the circumscribed circle inside or outside the trapezoid?
The center of the circle circumscribed around an obtuse triangle is located outside the triangle.

## Solution

By the external angle theorem of a triangle, we find that the diagonal forms an angle of $20^{\circ}$ with the larger base. Therefore, the larger base is seen from the vertex of the smaller base at an angle of

$$
180^{\circ}-\left(50^{\circ}+20^{\circ}\right)=110^{\circ}>90^{\circ} .
$$

Thus, the vertex of the upper base and the center of the circle lie in different half-planes relative to the line containing the larger base.

## Answer

Outside.