Question 127
Let $P$ be a point in the interior of triangle $ABC$. The lines $AP$, $BP$ and $CP$ meet the circumcircle $\Gamma$ of triangle $ABC$ again at $K$, $L$ and $M$ respectively. The tangent to $\Gamma$ at $C$ meets the line $AB$ at $S$. Prove that if $SC = SP$, then $MK = ML$.