Question 37
In the triangle $ABC$, the angle $\angle A$ is obtuse. Points $E$ and $F$ are the feet of the altitudes from $B$ and $C$, respectively. Tangents to the circumcircle of $ABC$ at $B$ and $C$ intersect the line $EF$ at points $K$ and $L$, respectively. Let $\angle CLB = 135^\circ$. Point $R$ lies on the segment $BK$ such that $KR = KL$. Point $S$ lies on the line $BK$ such that $K$ is between $B$ and $S$ and $\angle BLS = 135^\circ$. Prove that the circle with the diameter $RS$ is tangent to the circumcircle of $ABC$.