Question 2
Let $ABC$ be an acute angled triangle with $\angle B \gt \angle C$. Consider the points $D, E, J, K, S$ on its circumcircle $C(O)$, such that $A, E, J$ and $K$ are on the same side of the line $BC$, the diameter $DE$ and the line $BC$ are orthogonal, $S \in \widehat{EK}$ and $\widehat{AE} = \widehat{BJ} = \widehat{CK} = \frac{1}{4}\widehat{CE}$. Let $F, M, P, Q$ be the intersection points of the lines $AC$ and $DE$, $BK$ and $AD$, $BK$ and $AC$, $CJ$ and $BF$, respectively. If $\angle SMK = 30^\circ$ and $\angle AQP = 90^\circ$, prove that the line $MS$ is tangent to the circumcircle of the triangle $AOF$.
Dana Heuberger
Dana Heuberger