Question 3
Let $\Gamma$ be the circumcircle of triangle $ABC$. A circle through $A,C$ meets sides $BC,BA$ at $D,E$, respectively. Lines $AD,CE$ meet $\Gamma$ again at $G,H$, respectively. The tangents to $\Gamma$ at $A,C$ meet line $DE$ at $L,M$, respectively. Prove that lines $LH,MG$ meet at a point on $\Gamma$.
