Question 28
Let $ABC$ be a triangle with $AC \gt AB$, and $\Gamma$ its circumcircle. Let $T$ be the intersection point of the tangent to $\Gamma$ at $A$ with $(BC)$. Let $M$ be the midpoint of $[BC]$ and $R$ the reflection of $A$ across $B$. Let $S$ be the point such that $SABT$ is a parallelogram. The line parallel to $(AB)$ through $M$ meets $(SB)$ at $P$. Assuming that $P$ lies on $\Gamma$, show that $(AC)$ is tangent to the circumcircle of $SRT$.