NL-NWO 1986 Problem 4

The lines $a$ and $b$ are parallel and the point $A$ lies on $a$ . One chooses one circle $\gamma$ through A tangent to $b$ at $B$ . $a$ intersects $\gamma$ for the second time at $T$ . The tangent line at $T$ of $\gamma$ is called $t$ . Prove that independently of the choice of $\gamma$ , there is a fixed point $P$ such that $BT$ passes through $P$ . Prove that independently of the choice of $\gamma$ , there is a fixed circle $\delta$ such that $t$ is tangent to $\delta$ .