Question 82
Given a triangle $ABC$. A circle $k$ through $A$ and $B$ intersects the sides $AC$ and $BC$ at points $L$ and $N$, respectively. Let $M$ be the midpoint of the arc $LN$ lying in the triangle. Set $AM \cap BL = D$, $AM \cap BN = F$, $BM \cap AL = G$ and $BM \cap AN = E$. Prove that:
a) $DE\parallel FG$;
b) if $DEFG$ is a parallelogram, it is a rhombus.
a) $DE\parallel FG$;
b) if $DEFG$ is a parallelogram, it is a rhombus.