IMO Shortlist 2017 problem G2

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Let R and S be different points on a circle \Omega such that 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 the line segment RT. Point J is chosen on the shorter 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 that is closer to R. Line AJ meets \Omega again at K. Prove that the line KT is tangent to \Gamma.