DE-MO 2004 Problem 2

Let $k$ be a circle with center $M.$ There is another circle $k_1$ whose center $M_1$ lies on $k,$ and we denote the line through $M$ and $M_1$ by $g.$ Let $T$ be a point on $k_1$ and inside $k.$ The tangent $t$ to $k_1$ at $T$ intersects $k$ in two points $A$ and $B.$ Denote the tangents (diifferent from $t$ ) to $k_1$ passing through $A$ and $B$ by $a$ and $b$ , respectively. Prove that the lines $a,b,$ and $g$ are either concurrent or parallel.