Question 143
Let $ABCD$ be a cyclic quadrilateral and triangles $ACD$, $BCD$ are acute. Suppose that the lines $AB$ and $CD$ meet at $S$. Denote by $E$ the intersection of $AC$, $BD$. The circles $(ADE)$ and $(BCE)$ meet again at $F$.
1. Prove that $SF \perp EF$.
2. The point $G$ is taken outside of the quadrilateral $ABCD$ such that triangle $GAB$ and $FDC$ are similar. Prove that $GA + FB = GB + FA$.
1. Prove that $SF \perp EF$.
2. The point $G$ is taken outside of the quadrilateral $ABCD$ such that triangle $GAB$ and $FDC$ are similar. Prove that $GA + FB = GB + FA$.