Question 75
Let $ABC$ be a triangle with $AB \lt AC$ and $\omega$ be its circumcircle. The tangent at $A$ to the circle $\omega$ intersects line $BC$ at $D$, and the line through $B$ parallel to $AD$ meets again the circle $\omega$ at $E$. Line $DE$ intersects $AB$ at $F$ and the circle $\omega$ for the second time at $G$. On the line $BE$, consider the point $N$ such that $B, G, F$, and $N$ are con-cyclic. Let $S$ and $T$ be the intersection points of line $FN$ with $AD$ and $AE$, respectively. Prove that $STDG$ is a cyclic quadrilateral.
JBMO Shortlist
JBMO Shortlist