Question 84
Let $ABCD$ be a cyclic quadrilateral with $CD \lt AD$ and $CD \lt BC$. The diagonals $AC$ and $BD$ intersect at the point $S$. Let $e$ be the reflection of the line $AB$ in $AC$ and let $f$ be the reflection of the line $AB$ in $BD$. The line $CD$ meets $e$ and $f$ at the points $E$ and $F$, respectively. Prove that the triangle $SEF$ is isosceles.
Figure 1: Construction for the solution of Problem 3
Figure 1: Construction for the solution of Problem 3