Question 18
In the acute-angled triangle $ABP$ ($AB \gt BP$) the altitudes are $BH$, $PQ$ and $AS$. The extension of $QS$ intersects line $AP$ at $C$. The extension of $HS$ intersects $BC$ at $L$. If $HS = SL$ and $HL$ is perpendicular to $BC$, compute $\frac{SL}{SC}$.