Let $\displaystyle P $ be a point inside the triangle $\displaystyle ABC $ . The lines $\displaystyle AP , BP $ and $\displaystyle CP $ intersect the circumcircle $\displaystyle \Gamma$ of triangle $\displaystyle ABC$ agian at the points $\displaystyle K,L$ and $\displaystyle M$ respectively . The tagent to $\displaystyle \Gamma$ at $\displaystyle C$ intersects the line $\displaystyle AB$ at $\displaystyle S$ . Suppose that $\displaystyle SC = SP$ . Prove that $\displaystyle MK=ML$ .

If you could answer this problem , you are able to receive the Honourable Mention of this year IMO .