Consider two circles $S_{1}and{S}_2$ (externally touching) having centers at points A and B whose radii are 1 and 2 respectively. A tangent to circle $S_1$ from point B touch the circle $S_1$ at point C. The point D is chosen on circle $S_2$ so that  $\overline{AC}$ is parallel to $\overline{BD}$ and the two segments  $\overline{BC}$ and  $\overline{AD}$ do not intersect. Segment $\overline{AD}$ intersect the circle $S_1$ at E. the line through B and E intersects the circle $S_1$ at another point F. Then