Question 4
Let $R$ and $S$ be different points on a circle $\Omega$ such that $\overline{RS}$ is not a diameter. Let $\ell$ be the tangent line to $\Omega$ at $R$. Point $T$ is such that $S$ is the midpoint of $\overline{RT}$. Point $J$ is chosen on minor arc $RS$ of $\Omega$ so that the circumcircle $\Gamma$ of triangle $JST$ intersects $\ell$ at two distinct points. Let $A$ be the common point of $\Gamma$ and $\ell$ closer to $R$. Line $AJ$ meets $\Omega$ again at $K$. Prove that line $KT$ is tangent to $\Gamma$.