Question 64
Let $\overline{AC}$ be the diameter of the circle $k_1$ with the centre $B$. Circle $k_2$ touches the line $AC$ at the point $B$ and the circle $k_1$ at the point $D$. Tangent from $A$ (different from $AC$) to circle $k_2$ touches that circle at the point $E$ and intersects the line $BD$ in the point $F$. Determine the ratio $|AF| : |AB|$. (Hong Kong)