Question 38
A (convex) trapezoid $ABCD$ shall be called *good* if it is inscribed, has parallel sides $AB$ and $CD$, and $CD$ is shorter than $AB$. For a good trapezoid, we fix the following notations.
* The line parallel to $AD$ through $B$ intersects the line $CD$ in $S$.
* The tangents through $S$ to the circumcircle of the trapezoid meet the circumcircle in $E$ and $F$, respectively, where $E$ is on the same side of the line $CD$ as $A$.
Characterize good trapezoids $ABCD$ (in terms of the side lengths and/or angles of the trapezoid) for which the angles $\angle BSE$ and $\angle FSC$ are equal. The characterization should be as simple as possible.
* The line parallel to $AD$ through $B$ intersects the line $CD$ in $S$.
* The tangents through $S$ to the circumcircle of the trapezoid meet the circumcircle in $E$ and $F$, respectively, where $E$ is on the same side of the line $CD$ as $A$.
Characterize good trapezoids $ABCD$ (in terms of the side lengths and/or angles of the trapezoid) for which the angles $\angle BSE$ and $\angle FSC$ are equal. The characterization should be as simple as possible.