Question 8
Let $ABCD$ be a square, and let $k$ be the circle centred at $B$ passing through $A$, $C$ and the point $T$ inside the square. Tangent on $k$ at $T$ intersects the segments $\overline{CD}$ and $\overline{DA}$ at $E$ and $F$, respectively. Let $G$ and $H$ be the intersections of the lines $BE$ and $BF$ with the segment $\overline{AC}$, respectively.
Prove that the lines $BT$, $EH$ and $FG$ are passing through the same point.
Prove that the lines $BT$, $EH$ and $FG$ are passing through the same point.