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P,Q,R,P,Q,R,P,Q,R, and SSS are four coplaner points that lie on the sides AB‾,BC‾,CD‾,\overline{AB},\overline{BC},\overline{CD},AB,BC,CD, and DA‾,\overline{DA},DA, respectively, of a skew quadrilateral. Then what is ∣AP‾∣∣PB‾∣⋅∣BQ‾∣∣QC‾∣⋅∣CR‾∣∣RD‾∣⋅∣DS‾∣∣SA‾∣?\frac { \lvert\overline{AP}\rvert }{ \lvert\overline{PB}\rvert } \cdot \frac { \lvert\overline{BQ}\rvert }{ \lvert\overline{QC}\rvert } \cdot \frac { \lvert\overline{CR}\rvert }{ \lvert\overline{RD}\rvert } \cdot \frac { \lvert\overline{DS}\rvert }{ \lvert\overline{SA}\rvert }?∣PB∣∣AP∣⋅∣QC∣∣BQ∣⋅∣RD∣∣CR∣⋅∣SA∣∣DS∣?
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